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Kollepara PK, Chisholm RH, Kiss IZ, Miller JC. Ethical dilemma arises from optimizing interventions for epidemics in heterogeneous populations. J R Soc Interface 2024; 21:20230612. [PMID: 38320602 PMCID: PMC10846932 DOI: 10.1098/rsif.2023.0612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 01/04/2024] [Indexed: 02/08/2024] Open
Abstract
Interventions to mitigate the spread of infectious diseases, while succeeding in their goal, have economic and social costs associated with them. These limit the duration and intensity of the interventions. We study a class of interventions which reduce the reproduction number and find the optimal strength of the intervention which minimizes the final epidemic size for an immunity inducing infection. The intervention works by eliminating the overshoot part of an epidemic, and avoids a second wave of infections. We extend the framework by considering a heterogeneous population and find that the optimal intervention can pose an ethical dilemma for decision and policymakers. This ethical dilemma is shown to be analogous to the trolley problem. We apply this optimization strategy to real-world contact data and case fatality rates from three pandemics to underline the importance of this ethical dilemma in real-world scenarios.
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Affiliation(s)
- Pratyush K. Kollepara
- Department of Mathematical and Physical Sciences, La Trobe University, Melbourne, Australia
| | - Rebecca H. Chisholm
- Department of Mathematical and Physical Sciences, La Trobe University, Melbourne, Australia
- Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia
| | - István Z. Kiss
- Network Science Institute, Northeastern University London, London E1W 1LP, UK
| | - Joel C. Miller
- Department of Mathematical and Physical Sciences, La Trobe University, Melbourne, Australia
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Kiss IZ, Kurths J, Parlitz U, Sun J. Winners of 2022 Edward Norton Lorenz Early Career Awards. Chaos 2023; 33:110402. [PMID: 37910809 DOI: 10.1063/5.0182501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Accepted: 10/19/2023] [Indexed: 11/03/2023]
Affiliation(s)
- István Z Kiss
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam, Humboldt University Berlin, Berlin, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Jie Sun
- Huawei Hong Kong Research Center, N.T., Hong Kong SAR 999077, China
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Bomela W, Sebek M, Nagao R, Singhal B, Kiss IZ, Li JS. Finding influential nodes in networks using pinning control: Centrality measures confirmed with electrochemical oscillators. Chaos 2023; 33:093128. [PMID: 37729101 PMCID: PMC10513758 DOI: 10.1063/5.0163899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2023] [Accepted: 08/22/2023] [Indexed: 09/22/2023]
Abstract
The spatiotemporal organization of networks of dynamical units can break down resulting in diseases (e.g., in the brain) or large-scale malfunctions (e.g., power grid blackouts). Re-establishment of function then requires identification of the optimal intervention site from which the network behavior is most efficiently re-stabilized. Here, we consider one such scenario with a network of units with oscillatory dynamics, which can be suppressed by sufficiently strong coupling and stabilizing a single unit, i.e., pinning control. We analyze the stability of the network with hyperbolas in the control gain vs coupling strength state space and identify the most influential node (MIN) as the node that requires the weakest coupling to stabilize the network in the limit of very strong control gain. A computationally efficient method, based on the Moore-Penrose pseudoinverse of the network Laplacian matrix, was found to be efficient in identifying the MIN. In addition, we have found that in some networks, the MIN relocates when the control gain is changed, and thus, different nodes are the most influential ones for weakly and strongly coupled networks. A control theoretic measure is proposed to identify networks with unique or relocating MINs. We have identified real-world networks with relocating MINs, such as social and power grid networks. The results were confirmed in experiments with networks of chemical reactions, where oscillations in the networks were effectively suppressed through the pinning of a single reaction site determined by the computational method.
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Affiliation(s)
- Walter Bomela
- Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Michael Sebek
- Department of Physics and Center for Complex Network Research, Northeastern University, Boston, Massachusetts 02115, USA
| | - Raphael Nagao
- Institute of Chemistry, Department of Physical Chemistry, University of Campinas, Campinas, SP 13083-970, Brazil
| | - Bharat Singhal
- Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - István Z. Kiss
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
| | - Jr-Shin Li
- Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
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Kiss IZ, Kenah E, Rempała GA. Necessary and sufficient conditions for exact closures of epidemic equations on configuration model networks. J Math Biol 2023; 87:36. [PMID: 37532967 PMCID: PMC10397147 DOI: 10.1007/s00285-023-01967-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Revised: 05/09/2023] [Accepted: 07/11/2023] [Indexed: 08/04/2023]
Abstract
We prove that it is possible to obtain the exact closure of SIR pairwise epidemic equations on a configuration model network if and only if the degree distribution follows a Poisson, binomial, or negative binomial distribution. The proof relies on establishing the equivalence, for these specific degree distributions, between the closed pairwise model and a dynamical survival analysis (DSA) model that was previously shown to be exact. Specifically, we demonstrate that the DSA model is equivalent to the well-known edge-based Volz model. Using this result, we also provide reductions of the closed pairwise and Volz models to a single equation that involves only susceptibles. This equation has a useful statistical interpretation in terms of times to infection. We provide some numerical examples to illustrate our results.
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Affiliation(s)
- István Z Kiss
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK.
- Network Science Institute, Northeastern University London, London, E1W 1LP, UK.
| | - Eben Kenah
- Division of Biostatistics, College of Public Health and Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA
| | - Grzegorz A Rempała
- Division of Biostatistics, College of Public Health and Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA
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Ocampo-Espindola JL, Nikhil KL, Li JS, Herzog ED, Kiss IZ. Synchronization, clustering, and weak chimeras in a densely coupled transcription-based oscillator model for split circadian rhythms. Chaos 2023; 33:083105. [PMID: 37535024 PMCID: PMC10403273 DOI: 10.1063/5.0156135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2023] [Accepted: 07/08/2023] [Indexed: 08/04/2023]
Abstract
The synchronization dynamics for the circadian gene expression in the suprachiasmatic nucleus is investigated using a transcriptional circadian clock gene oscillator model. With global coupling in constant dark (DD) conditions, the model exhibits a one-cluster phase synchronized state, in dim light (dim LL), bistability between one- and two-cluster states and in bright LL, a two-cluster state. The two-cluster phase synchronized state, where some oscillator pairs synchronize in-phase, and some anti-phase, can explain the splitting of the circadian clock, i.e., generation of two bouts of daily activities with certain species, e.g., with hamsters. The one- and two-cluster states can be reached by transferring the animal from DD or bright LL to dim LL, i.e., the circadian synchrony has a memory effect. The stability of the one- and two-cluster states was interpreted analytically by extracting phase models from the ordinary differential equation models. In a modular network with two strongly coupled oscillator populations with weak intragroup coupling, with appropriate initial conditions, one group is synchronized to the one-cluster state and the other group to the two-cluster state, resulting in a weak-chimera state. Computational modeling suggests that the daily rhythms in sleep-wake depend on light intensity acting on bilateral networks of suprachiasmatic nucleus (SCN) oscillators. Addition of a network heterogeneity (coupling between the left and right SCN) allowed the system to exhibit chimera states. The simulations can guide experiments in the circadian rhythm research to explore the effect of light intensity on the complexities of circadian desynchronization.
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Affiliation(s)
| | - K. L. Nikhil
- Department of Biology, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130-4899, USA
| | - Jr-Shin Li
- Department of Electrical and Systems Engineering, Washington University in St Louis, 1 Brookings Drive, St. Louis, Missouri 63130, USA
| | - Erik D. Herzog
- Department of Biology, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130-4899, USA
| | - István Z. Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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Kiss IZ, Simon PL. On Parameter Identifiability in Network-Based Epidemic Models. Bull Math Biol 2023; 85:18. [PMID: 36705777 PMCID: PMC9880946 DOI: 10.1007/s11538-023-01121-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Accepted: 01/03/2023] [Indexed: 01/28/2023]
Abstract
Modelling epidemics on networks represents an important departure from classical compartmental models which assume random mixing. However, the resulting models are high-dimensional and their analysis is often out of reach. It turns out that mean-field models, low-dimensional systems of differential equations, whose variables are carefully chosen expected quantities from the exact model provide a good approximation and incorporate explicitly some network properties. Despite the emergence of such mean-field models, there has been limited work on investigating whether these can be used for inference purposes. In this paper, we consider network-based mean-field models and explore the problem of parameter identifiability when observations about an epidemic are available. Making use of the analytical tractability of most network-based mean-field models, e.g. explicit analytical expressions for leading eigenvalue and final epidemic size, we set up the parameter identifiability problem as finding the solution or solutions of a system of coupled equations. More precisely, subject to observing/measuring growth rate and final epidemic size, we seek to identify parameter values leading to these measurements. We are particularly concerned with disentangling transmission rate from the network density. To do this, we give a condition for practical identifiability and we find that except for the simplest model, parameters cannot be uniquely determined, that is, they are practically unidentifiable. This means that there exist multiple solutions (a manifold of infinite measure) which give rise to model output that is close to the data. Identifying, formalising and analytically describing this problem should lead to a better appreciation of the complexity involved in fitting models with many parameters to data.
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Affiliation(s)
- István Z. Kiss
- Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH UK
| | - Péter L. Simon
- Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary ,Numerical Analysis and Large Networks Research Group, ELKH-ELTE, Budapest, Hungary
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7
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Liu Y, Pérez-Mercader J, Kiss IZ. Synchronization of Belousov-Zhabotinsky oscillators with electrochemical coupling in a spontaneous process. Chaos 2022; 32:093128. [PMID: 36182363 DOI: 10.1063/5.0096689] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
A passive electrochemical coupling approach is proposed to induce spontaneous synchronization between chemical oscillators. The coupling exploits the potential difference between a catalyst redox couple in the Belousov-Zhabotinsky (BZ) reaction, without external feedback, to induce surface reactions that impact the kinetics of the bulk system. The effect of coupling in BZ oscillators under batch condition is characterized using phase synchronization measures. Although the frequency of the oscillators decreases nonlinearly over time, by a factor of 2 or more within 100 cycles, the coupling is strong enough to maintain synchronization. In such a highly drifting system, the Gibbs-Shannon entropy of the cyclic phase difference distribution can be used to quantify the coupling effect. We extend the Oregonator BZ model to account for the drifting natural frequencies in batch condition and for electrochemical coupling, and numerical simulations of the effect of acid concentration on synchronization patterns are in agreement with the experiments. Because of the passive nature of coupling, the proposed coupling scheme can open avenues for designing pattern recognition and neuromorphic computation systems using chemical reactions in a spontaneous process.
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Affiliation(s)
- Yifan Liu
- Department of Earth and Planetary Sciences, Harvard Origins of Life Initiative, Harvard University, 20 Oxford Street, Cambridge, Massachusetts 02138, USA
| | - Juan Pérez-Mercader
- Department of Earth and Planetary Sciences, Harvard Origins of Life Initiative, Harvard University, 20 Oxford Street, Cambridge, Massachusetts 02138, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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Nijholt E, Ocampo-Espindola JL, Eroglu D, Kiss IZ, Pereira T. Emergent hypernetworks in weakly coupled oscillators. Nat Commun 2022; 13:4849. [PMID: 35977934 PMCID: PMC9385626 DOI: 10.1038/s41467-022-32282-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2021] [Accepted: 07/25/2022] [Indexed: 11/30/2022] Open
Abstract
Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among oscillators, in spite that such models were originally defined as oscillator networks with pairwise interactions. Here, we show that hypernetworks can spontaneously emerge even in the presence of pairwise albeit nonlinear coupling given certain triplet frequency resonance conditions. The results are demonstrated in experiments with electrochemical oscillators and in simulations with integrate-and-fire neurons. By developing a comprehensive theory, we uncover the mechanism for emergent hypernetworks by identifying appearing and forbidden frequency resonant conditions. Furthermore, it is shown that microscopic linear (difference) coupling among units results in coupled mean fields, which have sufficient nonlinearity to facilitate hypernetworks. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict and engineer their emergence. Networks with higher-order interactions are relevant to variety of real-world applications, they can be good description of data even if the system has only pairwise interactions. The authors uncover the hypernetwork emergence in coupled nonlinear oscillators and electrochemical experiments.
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Affiliation(s)
- Eddie Nijholt
- Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, São Carlos, Brazil
| | | | - Deniz Eroglu
- Faculty of Engineering and Natural Sciences, Kadir Has University, Istanbul, Turkey
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, St. Louis, MO, USA
| | - Tiago Pereira
- Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, São Carlos, Brazil. .,Department of Mathematics, Imperial College London, London, UK.
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Abstract
We present a new method for analysing stochastic epidemic models under minimal assumptions. The method, dubbed dynamic survival analysis (DSA), is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of partial differential equations may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from foot-and-mouth disease in the UK (2001) and COVID-19 in India (2020) show good accuracy and confirm the method’s versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modelling, analysing and interpreting epidemic data with the help of the DSA approach.
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Affiliation(s)
| | | | - István Z Kiss
- Department of Mathematics, University of Sussex, Brighton, BN1 9RH, UK
| | - Eben Kenah
- Department of Biostatistics, The Ohio State University, Columbus, OH 43210, USA
| | - Max Jensen
- Department of Mathematics, University of Sussex, Brighton, BN1 9RH, UK
| | - Grzegorz A Rempała
- Department of Biostatistics, The Ohio State University, Columbus, OH 43210, USA
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Zerenner T, Di Lauro F, Dashti M, Berthouze L, Kiss IZ. Probabilistic predictions of SIS epidemics on networks based on population-level observations. Math Biosci 2022; 350:108854. [PMID: 35659615 DOI: 10.1016/j.mbs.2022.108854] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Revised: 05/17/2022] [Accepted: 05/23/2022] [Indexed: 11/16/2022]
Abstract
We predict the future course of ongoing susceptible-infected-susceptible (SIS) epidemics on regular, Erdős-Rényi and Barabási-Albert networks. It is known that the contact network influences the spread of an epidemic within a population. Therefore, observations of an epidemic, in this case at the population-level, contain information about the underlying network. This information, in turn, is useful for predicting the future course of an ongoing epidemic. To exploit this in a prediction framework, the exact high-dimensional stochastic model of an SIS epidemic on a network is approximated by a lower-dimensional surrogate model. The surrogate model is based on a birth-and-death process; the effect of the underlying network is described by a parametric model for the birth rates. We demonstrate empirically that the surrogate model captures the intrinsic stochasticity of the epidemic once it reaches a point from which it will not die out. Bayesian parameter inference allows for uncertainty about the model parameters and the class of the underlying network to be incorporated directly into probabilistic predictions. An evaluation of a number of scenarios shows that in most cases the resulting prediction intervals adequately quantify the prediction uncertainty. As long as the population-level data is available over a long-enough period, even if not sampled frequently, the model leads to excellent predictions where the underlying network is correctly identified and prediction uncertainty mainly reflects the intrinsic stochasticity of the spreading epidemic. For predictions inferred from shorter observational periods, uncertainty about parameters and network class dominate prediction uncertainty. The proposed method relies on minimal data at population-level, which is always likely to be available. This, combined with its numerical efficiency, makes the proposed method attractive to be used either as a standalone inference and prediction scheme or in conjunction with other inference and/or predictive models.
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Affiliation(s)
- T Zerenner
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK.
| | - F Di Lauro
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK; Big Data Institute, Nuffield Department of Medicine, University of Oxford, Oxford, OX3 7FL, UK
| | - M Dashti
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK
| | - L Berthouze
- Department of Informatics, University of Sussex, Falmer, Brighton, BN1 9QH, UK
| | - I Z Kiss
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK.
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Backhausz Á, Kiss IZ, Simon PL. The impact of spatial and social structure on an SIR epidemic on a weighted multilayer network. Period Math Hung 2022; 85:343-363. [PMID: 35013623 PMCID: PMC8733920 DOI: 10.1007/s10998-021-00440-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 05/18/2021] [Indexed: 06/14/2023]
Abstract
A key factor in the transmission of infectious diseases is the structure of disease transmitting contacts. In the context of the current COVID-19 pandemic and with some data based on the Hungarian population we develop a theoretical epidemic model (susceptible-infected-removed, SIR) on a multilayer network. The layers include the Hungarian household structure, with population divided into children, adults and elderly, as well as schools and workplaces, some spatial embedding and community transmission due to sharing communal spaces, service and public spaces. We investigate the sensitivity of the model (via the time evolution and final size of the epidemic) to the different contact layers and we map out the relation between peak prevalence and final epidemic size. When compared to the classic compartmental model and for the same final epidemic size, we find that epidemics on multilayer network lead to higher peak prevalence meaning that the risk of overwhelming the health care system is higher. Based on our model we found that keeping cliques/bubbles in school as isolated as possible has a major effect while closing workplaces had a mild effect as long as workplaces are of relatively small size.
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Affiliation(s)
- Ágnes Backhausz
- Institute of Mathematics, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/c, Budapest, 1117 Hungary
- Alfréd Rényi Institute of Matematics, Reáltanoda utca 13-15, Budapest, 1053 Hungary
| | - István Z. Kiss
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, BN1 9QH United Kingdom
| | - Péter L. Simon
- Institute of Mathematics, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/c, Budapest, 1117 Hungary
- Numerical Analysis and Large Networks Research Group, Hungarian Academy of Sciences, Pázmány Péter sétány 1/c, Budapest, 1117 Hungary
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Eroglu D, Peron TKD, Marwan N, Rodrigues FA, Costa LDF, Sebek M, Kiss IZ, Kurths J. Publisher's Note: Entropy of weighted recurrence plots [Phys. Rev. E 90, 042919 (2014)]. Phys Rev E 2021; 104:039904. [PMID: 34654215 DOI: 10.1103/physreve.104.039904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Indexed: 11/07/2022]
Abstract
This corrects the article DOI: 10.1103/PhysRevE.90.042919.
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Di Lauro F, Berthouze L, Dorey MD, Miller JC, Kiss IZ. The Impact of Contact Structure and Mixing on Control Measures and Disease-Induced Herd Immunity in Epidemic Models: A Mean-Field Model Perspective. Bull Math Biol 2021; 83:117. [PMID: 34654959 PMCID: PMC8518901 DOI: 10.1007/s11538-021-00947-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Accepted: 09/27/2021] [Indexed: 11/27/2022]
Abstract
The contact structure of a population plays an important role in transmission of infection. Many 'structured models' capture aspects of the contact pattern through an underlying network or a mixing matrix. An important observation in unstructured models of a disease that confers immunity is that once a fraction [Formula: see text] has been infected, the residual susceptible population can no longer sustain an epidemic. A recent observation of some structured models is that this threshold can be crossed with a smaller fraction of infected individuals, because the disease acts like a targeted vaccine, preferentially immunising higher-risk individuals who play a greater role in transmission. Therefore, a limited 'first wave' may leave behind a residual population that cannot support a second wave once interventions are lifted. In this paper, we set out to investigate this more systematically. While networks offer a flexible framework to model contact patterns explicitly, they suffer from several shortcomings: (i) high-fidelity network models require a large amount of data which can be difficult to harvest, and (ii) very few, if any, theoretical contact network models offer the flexibility to tune different contact network properties within the same framework. Therefore, we opt to systematically analyse a number of well-known mean-field models. These are computationally efficient and provide good flexibility in varying contact network properties such as heterogeneity in the number contacts, clustering and household structure or differentiating between local and global contacts. In particular, we consider the question of herd immunity under several scenarios. When modelling interventions as changes in transmission rates, we confirm that in networks with significant degree heterogeneity, the first wave of the epidemic confers herd immunity with significantly fewer infections than equivalent models with less or no degree heterogeneity. However, if modelling the intervention as a change in the contact network, then this effect may become much more subtle. Indeed, modifying the structure disproportionately can shield highly connected nodes from becoming infected during the first wave and therefore make the second wave more substantial. We strengthen this finding by using an age-structured compartmental model parameterised with real data and comparing lockdown periods implemented either as a global scaling of the mixing matrix or age-specific structural changes. Overall, we find that results regarding (disease-induced) herd immunity levels are strongly dependent on the model, the duration of the lockdown and how the lockdown is implemented in the model.
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Affiliation(s)
- Francesco Di Lauro
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, BN1 9QH, UK
| | - Luc Berthouze
- Department of Informatics, School of Engineering and Informatics, University of Sussex, Falmer, Brighton, BN1 9QH, UK
| | - Matthew D Dorey
- Public Health and Social Research Unit, West Sussex County Council, Tower Street, Chichester, P019 1RQ, UK
| | - Joel C Miller
- Department of Mathematics and Statistics, School of Engineering and Mathematical Sciences, La Trobe University, Bundoora, Australia
| | - István Z Kiss
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, BN1 9QH, UK.
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Omel'chenko OE, Ocampo-Espindola JL, Kiss IZ. Asymmetry-induced isolated fully synchronized state in coupled oscillator populations. Phys Rev E 2021; 104:L022202. [PMID: 34525593 DOI: 10.1103/physreve.104.l022202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Accepted: 07/04/2021] [Indexed: 11/07/2022]
Abstract
A symmetry-breaking mechanism is investigated that creates bistability between fully and partially synchronized states in oscillator networks. Two populations of oscillators with unimodal frequency distribution and different amplitudes, in the presence of weak global coupling, are shown to simplify to a modular network with asymmetrical coupling. With increasing the coupling strength, a synchronization transition is observed with an isolated fully synchronized state. The results are interpreted theoretically in the thermodynamic limit and confirmed in experiments with chemical oscillators.
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Affiliation(s)
- Oleh E Omel'chenko
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam, Germany
| | | | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
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15
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Magrini LA, Oliveira Domingues M, Macau EEN, Kiss IZ. Synchronization in populations of electrochemical bursting oscillators with chaotic slow dynamics. Chaos 2021; 31:053125. [PMID: 34240953 DOI: 10.1063/5.0041488] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Accepted: 04/27/2021] [Indexed: 06/13/2023]
Abstract
We investigate the synchronization of coupled electrochemical bursting oscillators using the electrodissolution of iron in sulfuric acid. The dynamics of a single oscillator consisted of slow chaotic oscillations interrupted by a burst of fast spiking, generating a multiple time-scale dynamical system. A wavelet analysis first decomposed the time series data from each oscillator into a fast and a slow component, and the corresponding phases were also obtained. The phase synchronization of the fast and slow dynamics was analyzed as a function of electrical coupling imposed by an external coupling resistance. For two oscillators, a progressive transition was observed: With increasing coupling strength, first, the fast bursting intervals overlapped, which was followed by synchronization of the fast spiking, and finally, the slow chaotic oscillations synchronized. With a population of globally coupled 25 oscillators, the coupling eliminated the fast dynamics, and only the synchronization of the slow dynamics can be observed. The results demonstrated the complexities of synchronization with bursting oscillations that could be useful in other systems with multiple time-scale dynamics, in particular, in neuronal networks.
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Affiliation(s)
- Luciano A Magrini
- Federal Institute of Education, Science and Technology of São Paulo (IFSP), Votuporanga 15503-110, Brazil
| | | | - Elbert E N Macau
- Federal University of São Paulo at São José dos Campos (UNIFESP), São José dos Campos 12231-280, Brazil
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St Louis, Missouri 63103, USA
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16
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Di Lauro F, Kiss IZ, Miller JC. Optimal timing of one-shot interventions for epidemic control. PLoS Comput Biol 2021; 17:e1008763. [PMID: 33735171 PMCID: PMC8009413 DOI: 10.1371/journal.pcbi.1008763] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2020] [Revised: 03/30/2021] [Accepted: 02/02/2021] [Indexed: 01/08/2023] Open
Abstract
The interventions and outcomes in the ongoing COVID-19 pandemic are highly varied. The disease and the interventions both impose costs and harm on society. Some interventions with particularly high costs may only be implemented briefly. The design of optimal policy requires consideration of many intervention scenarios. In this paper we investigate the optimal timing of interventions that are not sustainable for a long period. Specifically, we look at at the impact of a single short-term non-repeated intervention (a "one-shot intervention") on an epidemic and consider the impact of the intervention's timing. To minimize the total number infected, the intervention should start close to the peak so that there is minimal rebound once the intervention is stopped. To minimise the peak prevalence, it should start earlier, leading to initial reduction and then having a rebound to the same prevalence as the pre-intervention peak rather than one very large peak. To delay infections as much as possible (as might be appropriate if we expect improved interventions or treatments to be developed), earlier interventions have clear benefit. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each subcommunity separately.
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Affiliation(s)
- Francesco Di Lauro
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton United Kingdom
| | - István Z. Kiss
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton United Kingdom
| | - Joel C. Miller
- Department of Mathematics and Statistics, School of Engineering and Mathematical Sciences, La Trobe University, Bundoora, Australia
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17
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Di Lauro F, Croix JC, Dashti M, Berthouze L, Kiss IZ. Network inference from population-level observation of epidemics. Sci Rep 2020; 10:18779. [PMID: 33139773 PMCID: PMC7606546 DOI: 10.1038/s41598-020-75558-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2020] [Accepted: 09/21/2020] [Indexed: 12/03/2022] Open
Abstract
Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem of inferring the class of the underlying network when epidemic data is only available at population-level (i.e., the number of infected individuals at a finite set of discrete times of a single realisation of the epidemic), the only information likely to be available in real world settings. To tackle this, epidemics on networks are approximated by a Birth-and-Death process which keeps track of the number of infected nodes at population level. The rates of this surrogate model encode both the structure of the underlying network and disease dynamics. We use extensive simulations over Regular, Erdős–Rényi and Barabási–Albert networks to build network class-specific priors for these rates. We then use Bayesian model selection to recover the most likely underlying network class, based only on a single realisation of the epidemic. We show that the proposed methodology yields good results on both synthetic and real-world networks.
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Affiliation(s)
- F Di Lauro
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK
| | - J-C Croix
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK
| | - M Dashti
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK
| | - L Berthouze
- Department of Informatics, University of Sussex, Falmer, BN1 9QH, UK
| | - I Z Kiss
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK.
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18
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Nicolaou ZG, Sebek M, Kiss IZ, Motter AE. Coherent Dynamics Enhanced by Uncorrelated Noise. Phys Rev Lett 2020; 125:094101. [PMID: 32915595 DOI: 10.1103/physrevlett.125.094101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2020] [Revised: 06/17/2020] [Accepted: 07/21/2020] [Indexed: 06/11/2023]
Abstract
Synchronization is a widespread phenomenon observed in physical, biological, and social networks, which persists even under the influence of strong noise. Previous research on oscillators subject to common noise has shown that noise can actually facilitate synchronization, as correlations in the dynamics can be inherited from the noise itself. However, in many spatially distributed networks, such as the mammalian circadian system, the noise that different oscillators experience can be effectively uncorrelated. Here, we show that uncorrelated noise can in fact enhance synchronization when the oscillators are coupled. Strikingly, our analysis also shows that uncorrelated noise can be more effective than common noise in enhancing synchronization. We first establish these results theoretically for phase and phase-amplitude oscillators subject to either or both additive and multiplicative noise. We then confirm the predictions through experiments on coupled electrochemical oscillators. Our findings suggest that uncorrelated noise can promote rather than inhibit coherence in natural systems and that the same effect can be harnessed in engineered systems.
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Affiliation(s)
- Zachary G Nicolaou
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
- Network Science Institute, Northeastern University, Boston, Massachusetts 02115, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
| | - Adilson E Motter
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
- Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA
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19
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Thompson RN, Hollingsworth TD, Isham V, Arribas-Bel D, Ashby B, Britton T, Challenor P, Chappell LHK, Clapham H, Cunniffe NJ, Dawid AP, Donnelly CA, Eggo RM, Funk S, Gilbert N, Glendinning P, Gog JR, Hart WS, Heesterbeek H, House T, Keeling M, Kiss IZ, Kretzschmar ME, Lloyd AL, McBryde ES, McCaw JM, McKinley TJ, Miller JC, Morris M, O'Neill PD, Parag KV, Pearson CAB, Pellis L, Pulliam JRC, Ross JV, Tomba GS, Silverman BW, Struchiner CJ, Tildesley MJ, Trapman P, Webb CR, Mollison D, Restif O. Key questions for modelling COVID-19 exit strategies. Proc Biol Sci 2020; 287:20201405. [PMID: 32781946 PMCID: PMC7575516 DOI: 10.1098/rspb.2020.1405] [Citation(s) in RCA: 74] [Impact Index Per Article: 18.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2020] [Accepted: 07/21/2020] [Indexed: 12/15/2022] Open
Abstract
Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.
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Affiliation(s)
- Robin N. Thompson
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
- Christ Church, University of Oxford, St Aldates, Oxford OX1 1DP, UK
- Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
| | | | - Valerie Isham
- Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK
| | - Daniel Arribas-Bel
- School of Environmental Sciences, University of Liverpool, Brownlow Street, Liverpool L3 5DA, UK
- The Alan Turing Institute, British Library, 96 Euston Road, London NW1 2DB, UK
| | - Ben Ashby
- Department of Mathematical Sciences, University of Bath, North Road, Bath BA2 7AY, UK
| | - Tom Britton
- Department of Mathematics, Stockholm University, Kräftriket, 106 91 Stockholm, Sweden
| | - Peter Challenor
- College of Engineering, Mathematical and Physical Sciences, University of Exeter, Exeter EX4 4QE, UK
| | - Lauren H. K. Chappell
- Department of Plant Sciences, University of Oxford, South Parks Road, Oxford OX1 3RB, UK
| | - Hannah Clapham
- Saw Swee Hock School of Public Health, National University of Singapore, 12 Science Drive, Singapore117549, Singapore
| | - Nik J. Cunniffe
- Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, UK
| | - A. Philip Dawid
- Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK
| | - Christl A. Donnelly
- Department of Statistics, University of Oxford, St Giles', Oxford OX1 3LB, UK
- MRC Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, Imperial CollegeLondon, Norfolk Place, London W2 1PG, UK
| | - Rosalind M. Eggo
- Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
| | - Sebastian Funk
- Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
| | - Nigel Gilbert
- Department of Sociology, University of Surrey, Stag Hill, Guildford GU2 7XH, UK
| | - Paul Glendinning
- Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Julia R. Gog
- Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - William S. Hart
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
| | - Hans Heesterbeek
- Department of Population Health Sciences, Utrecht University, Yalelaan, 3584 CL Utrecht, The Netherlands
| | - Thomas House
- IBM Research, The Hartree Centre, Daresbury, Warrington WA4 4AD, UK
- Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
| | - Matt Keeling
- Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, School of Life Sciences and Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
| | - István Z. Kiss
- School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK
| | - Mirjam E. Kretzschmar
- Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht University, Heidelberglaan 100, 3584CX Utrecht, The Netherlands
| | - Alun L. Lloyd
- Biomathematics Graduate Program and Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
| | - Emma S. McBryde
- Australian Institute of Tropical Health and Medicine, James Cook University, Townsville, Queensland 4811, Australia
| | - James M. McCaw
- School of Mathematics and Statistics, University of Melbourne, Carlton, Victoria 3010, Australia
| | - Trevelyan J. McKinley
- College of Medicine and Health, University of Exeter, Barrack Road, Exeter EX2 5DW, UK
| | - Joel C. Miller
- Department of Mathematics and Statistics, La Trobe University, Bundoora, Victoria 3086, Australia
| | - Martina Morris
- Department of Sociology, University of Washington, Savery Hall, Seattle, WA 98195, USA
| | - Philip D. O'Neill
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
| | - Kris V. Parag
- MRC Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, Imperial CollegeLondon, Norfolk Place, London W2 1PG, UK
| | - Carl A. B. Pearson
- Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
- South African DSI-NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, Jonkershoek Road, Stellenbosch 7600, South Africa
| | - Lorenzo Pellis
- Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Juliet R. C. Pulliam
- South African DSI-NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, Jonkershoek Road, Stellenbosch 7600, South Africa
| | - Joshua V. Ross
- School of Mathematical Sciences, University of Adelaide, South Australia 5005, Australia
| | | | - Bernard W. Silverman
- Department of Statistics, University of Oxford, St Giles', Oxford OX1 3LB, UK
- Rights Lab, University of Nottingham, Highfield House, Nottingham NG7 2RD, UK
| | - Claudio J. Struchiner
- Escola de Matemática Aplicada, Fundação Getúlio Vargas, Praia de Botafogo, 190 Rio de Janeiro, Brazil
| | - Michael J. Tildesley
- Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, School of Life Sciences and Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
| | - Pieter Trapman
- Department of Mathematics, Stockholm University, Kräftriket, 106 91 Stockholm, Sweden
| | - Cerian R. Webb
- Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, UK
| | - Denis Mollison
- Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, UK
| | - Olivier Restif
- Department of Veterinary Medicine, University of Cambridge, Madingley Road, Cambridge CB3 0ES, UK
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A Magrini L, Oliveira Domingues M, Macau EEN, Kiss IZ. Extraction of slow and fast dynamics of multiple time scale systems using wavelet techniques. Chaos 2020; 30:063139. [PMID: 32611096 DOI: 10.1063/5.0004719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Accepted: 06/01/2020] [Indexed: 06/11/2023]
Abstract
A methodology is presented based on wavelet techniques to approximate fast and slow dynamics present in time-series whose behavior is characterized by different local scales in time. These approximations are useful to understand the global dynamics of the original full systems, especially in experimental situations where all information is contained in a one-dimensional time-series. Wavelet analysis is a natural approach to handle these approximations because each dynamical behavior manifests its specific subset in frequency domain, for example, with two time scales, the slow and fast dynamics, present in low and high frequencies, respectively. The proposed procedure is illustrated by the analysis of a complex experimental time-series of iron electrodissolution where the slow chaotic dynamics is interrupted by fast irregular spiking. The method can be used to first filter the time-series data and then separate the fast and slow dynamics even when clear maxima and/or minima in the corresponding global wavelet spectrum are missing. The results could find applications in the analysis of synchronization of complex systems through multi-scale analysis.
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Affiliation(s)
- Luciano A Magrini
- Federal Institute of Education, Science and Technology of São Paulo (IFSP), São Paulo 01109-010, Brazil
| | | | - Elbert E N Macau
- Associated Laboratory of Computation and Applied Mathematics (LabAC), São José dos Campos 12227-010, Brazil
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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21
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Sebek M, Kawamura Y, Nott AM, Kiss IZ. Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators. Philos Trans A Math Phys Eng Sci 2019; 377:20190095. [PMID: 31656145 PMCID: PMC6833994 DOI: 10.1098/rsta.2019.0095] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/05/2019] [Indexed: 05/02/2023]
Abstract
The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.
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Affiliation(s)
- Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA
| | - Yoji Kawamura
- Center for Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, 236-0001 Yokohama, Japan
| | - Ashley M. Nott
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA
| | - István Z. Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA
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22
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Sebek M, Kiss IZ. Plasticity facilitates pattern selection of networks of chemical oscillations. Chaos 2019; 29:083117. [PMID: 31472493 DOI: 10.1063/1.5109784] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2019] [Accepted: 07/22/2019] [Indexed: 06/10/2023]
Abstract
Rotating wave synchronization patterns are explored with a ring of 20 electrochemical oscillators during nickel electrodissolution in sulfuric acid. With desynchronized initial states, coupling alone yields predominance of nonrotating solutions, i.e., in-phase synchronization. An experimental technique is presented in which, through a combination of temporary alterations in topology, the application of global feedback provides rotational solutions. With phase repulsive global feedback, the in-phase synchronization is destabilized and a rotating wave is obtained. This feedback induced rotating wave can be employed to establish an initial condition for the rotating wave with coupling only. Higher order rotating solutions with 2, 3, and 4 waves corotating around the ring are observed, where the initial conditions are generated by temporary network rewiring to a structure with 2, 3, and 4 loops, respectively, and by global feedback. The experimental observations are supported by numerical simulations with a phase model. The results indicate that while network plasticity is thought to be significant in the operation of neural systems, it can also play a role in pattern selection of chemical systems.
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Affiliation(s)
- Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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23
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Barnard RC, Berthouze L, Simon PL, Kiss IZ. Epidemic threshold in pairwise models for clustered networks: closures and fast correlations. J Math Biol 2019; 79:823-860. [PMID: 31079178 PMCID: PMC6667428 DOI: 10.1007/s00285-019-01380-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2018] [Revised: 05/01/2019] [Indexed: 11/09/2022]
Abstract
The epidemic threshold is probably the most studied quantity in the modelling of epidemics on networks. For a large class of networks and dynamics, it is well studied and understood. However, it is less so for clustered networks where theoretical results are mostly limited to idealised networks. In this paper we focus on a class of models known as pairwise models where, to our knowledge, no analytical result for the epidemic threshold exists. We show that by exploiting the presence of fast variables and using some standard techniques from perturbation theory we are able to obtain the epidemic threshold analytically. We validate this new threshold by comparing it to the threshold based on the numerical solution of the full system. The agreement is found to be excellent over a wide range of values of the clustering coefficient, transmission rate and average degree of the network. Interestingly, we find that the analytical form of the threshold depends on the choice of closure, highlighting the importance of model selection when dealing with real-world epidemics. Nevertheless, we expect that our method will extend to other systems in which fast variables are present.
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Affiliation(s)
- Rosanna C Barnard
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, BN1 9QH, UK
| | - Luc Berthouze
- Centre for Computational Neuroscience and Robotics, University of Sussex, Falmer, Brighton, BN1 9QH, UK
| | - Péter L Simon
- Institute of Mathematics, Eötvös Loránd University Budapest, Budapest, Hungary.,Numerical Analysis and Large Networks Research Group, Hungarian Academy of Sciences, Budapest, Hungary
| | - István Z Kiss
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, BN1 9QH, UK.
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24
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Hankins MJ, Gáspár V, Kiss IZ. Abrupt and gradual onset of synchronized oscillations due to dynamical quorum sensing in the single-cathode multi-anode nickel electrodissolution system. Chaos 2019; 29:033114. [PMID: 30927839 DOI: 10.1063/1.5087405] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2018] [Accepted: 02/19/2019] [Indexed: 06/09/2023]
Abstract
The nonlinear dynamics of an oscillatory Ni electrodissolution-hydrogen ion reduction system are explored in a multi-electrode anode-single cathode system. A mathematical analysis of the charge balance equations reveals that the coupling scheme is similar to dynamical quorum sensing, where the number of anode wires affects a parameter related to the population density. In a parameter region where the large population exhibits stationary behavior, with sufficiently strong coupling (with small individual resistances attached to the anode wires), synchronized oscillations emerge abruptly with decreasing the number of anodes. Therefore, an "inverse" dynamical quorum sensing takes place. With weak coupling the transition is gradual. The experiments are supported by numerical simulation of a kinetic model of the process. The results thus show that the description of nontrivial cathode-anode interactions in the form of dynamical quorum sensing provides an efficient way of analyzing the dynamical response of complex, interacting electrochemical reactions.
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Affiliation(s)
- Michael J Hankins
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
| | - Vilmos Gáspár
- Laboratory of Nonlinear Chemical Dynamics, Institute of Chemistry, Eötvös Loránd University, Pázmány P. sétány 1/A, Budapest 1117, Hungary
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
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25
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Zou W, Ocampo-Espindola JL, Senthilkumar DV, Kiss IZ, Zhan M, Kurths J. Quenching and revival of oscillations induced by coupling through adaptive variables. Phys Rev E 2019; 99:032214. [PMID: 30999495 DOI: 10.1103/physreve.99.032214] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Indexed: 06/09/2023]
Abstract
An adaptive coupling based on a low-pass filter (LPF) is proposed to manipulate dynamic activity of diffusively coupled dynamical systems. A theoretical analysis shows that tracking either the external or internal signal in the coupling via a LPF gives rise to distinctly different ways of regulating the rhythmicity of the coupled systems. When the external signals of the coupling are attenuated by a LPF, the macroscopic oscillations of the coupled system are quenched due to the emergence of amplitude or oscillation death. If the internal signals of the coupling are further filtered by a LPF, amplitude and oscillation deaths are effectively revoked to restore dynamic behaviors. The applicability of this approach is demonstrated in laboratory experiments of coupled oscillatory electrochemical reactions by inducing coupling through LPFs. Our study provides additional insight into (ar)rhythmogenesis in diffusively coupled systems.
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Affiliation(s)
- Wei Zou
- School of Mathematical Sciences, South China Normal University, Guangzhou 510631, People's Republic of China
| | | | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695551, India
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - Meng Zhan
- School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany
- Institute of Physics, Humboldt University Berlin, Berlin D-12489, Germany
- Saratov State University, Saratov 4410012, Russia
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27
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Dahlhaus R, Kiss IZ, Neddermeyer JC. On the Relationship between the Theory of Cointegration and the Theory of Phase Synchronization. Stat Sci 2018. [DOI: 10.1214/18-sts659] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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28
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Omel'chenko OE, Sebek M, Kiss IZ. Universal relations of local order parameters for partially synchronized oscillators. Phys Rev E 2018; 97:062207. [PMID: 30011585 DOI: 10.1103/physreve.97.062207] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2018] [Indexed: 11/07/2022]
Abstract
Interactions among discrete oscillatory units (e.g., cells) can result in partially synchronized states when some of the units exhibit phase locking and others phase slipping. Such states are typically characterized by a global order parameter that expresses the extent of synchrony in the system. Here we show that such states carry data-rich information of the system behavior, and a local order parameter analysis reveals universal relations through a semicircle representation. The universal relations are derived from thermodynamic limit analysis of a globally coupled Kuramoto-type phase oscillator model. The relations are confirmed with the partially synchronized states in numerical simulations with a model of circadian cells and in laboratory experiments with chemical oscillators. The application of the theory allows direct approximation of coupling strength, the natural frequency of oscillations, and the phase lag parameter without extensive nonlinear fits as well as a self-consistency check for presence of network interactions and higher harmonic components in the phase model.
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Affiliation(s)
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
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29
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Affiliation(s)
- Walter B. Bomela
- Washington University in St. Louis, St. Louis, Missouri 63130, United States
| | - Isuru S. Dasanayake
- Washington University in St. Louis, St. Louis, Missouri 63130, United States
| | - Jr-Shin Li
- Washington University in St. Louis, St. Louis, Missouri 63130, United States
| | - Yifei Chen
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, United States
| | - István Z. Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, United States
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Kori H, Kiss IZ, Jain S, Hudson JL. Partial synchronization of relaxation oscillators with repulsive coupling in autocatalytic integrate-and-fire model and electrochemical experiments. Chaos 2018; 28:045111. [PMID: 31906647 DOI: 10.1063/1.5022497] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters and desynchronized states, repulsive coupling results in synchronized oscillations. The experiments are interpreted with a phenomenological model that captures the waveform of the oscillations (exponential increase) followed by a refractory period. The globally coupled autocatalytic integrate-and-fire model predicts the development of partially synchronized states that occur through attracting heteroclinic cycles between out-of-phase two-cluster states. Similar behavior can be expected in many other systems where the oscillations occur close to a saddle-loop bifurcation, e.g., with Morris-Lecar neurons.
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Affiliation(s)
- Hiroshi Kori
- Department of Information Sciences, Ochanomizu University, Tokyo 112-8610, Japan
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
| | - Swati Jain
- Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
| | - John L Hudson
- Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
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Abstract
The spread of an infectious disease is known to change people's behavior, which in turn affects the spread of disease. Adaptive network models that account for both epidemic and behavioral change have found oscillations, but in an extremely narrow region of the parameter space, which contrasts with intuition and available data. In this paper we propose a simple susceptible-infected-susceptible epidemic model on an adaptive network with time-delayed rewiring, and show that oscillatory solutions are now present in a wide region of the parameter space. Altering the transmission or rewiring rates reveals the presence of an endemic bubble—an enclosed region of the parameter space where oscillations are observed.
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Affiliation(s)
- N Sherborne
- Department of Mathematics, University of Sussex, Brighton BN1 9QH, England, United Kingdom
| | - K B Blyuss
- Department of Mathematics, University of Sussex, Brighton BN1 9QH, England, United Kingdom
| | - I Z Kiss
- Department of Mathematics, University of Sussex, Brighton BN1 9QH, England, United Kingdom
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Abstract
We investigate the formation of synchronization patterns in an oscillatory nickel electrodissolution system in a network obtained by superimposing local and global coupling with three electrodes. We explored the behavior through numerical simulations using kinetic ordinary differential equations, Kuramoto type phase models, and experiments, in which the local to global coupling could be tuned by cross resistances between the three nickel wires. At intermediate coupling strength with predominant global coupling, two of the three oscillators, whose natural frequencies are closer, can synchronize. By adding even a relatively small amount of local coupling (about 9%-25%), a spatially organized partially synchronized state can occur where one of the two synchronized elements is in the center. A formula was derived for predicting the critical coupling strength at which full synchronization will occur independent of the permutation of the natural frequencies of the oscillators over the network. The formula correctly predicts the variation of the critical coupling strength as a function of the global coupling fraction, e.g., with local coupling the critical coupling strength is about twice than that required with global coupling. The results show the importance of the topology of the network on the synchronization properties in a simple three-oscillator setup and could provide guidelines for decrypting coupling topology from identification of synchronization patterns.
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Affiliation(s)
- Yifan Liu
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - Fumito Mori
- Theoretical Biology Laboratory, RIKEN, Wako 351-0198, Japan
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
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Kevrekidis YG, Kiss IZ, Kori H, Krischer K. Introduction to Focus Issue: In Memory of John L. Hudson: Self-Organized Structures in Chemical Systems. Chaos 2018; 28:045001. [PMID: 31906653 DOI: 10.1063/1.5033452] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Affiliation(s)
- Yannis G Kevrekidis
- Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - Hiroshi Kori
- Department of Information Sciences, Ochanomizu University, Tokyo 112-8610, Japan
| | - Katharina Krischer
- Department of Physics, Technical University of Munich, James-Franck-Str. 1, D-85748 Garching, Germany
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34
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Affiliation(s)
- Michael Sebek
- Department of Chemistry Saint Louis University 3501 Laclede Ave. St. Louis MO 63103 USA
| | - István Z. Kiss
- Department of Chemistry Saint Louis University 3501 Laclede Ave. St. Louis MO 63103 USA
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35
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Röst G, Vizi Z, Kiss IZ. Pairwise approximation for SIR-type network epidemics with non-Markovian recovery. Proc Math Phys Eng Sci 2018; 474:20170695. [PMID: 29507514 DOI: 10.1098/rspa.2017.0695] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2017] [Accepted: 01/25/2018] [Indexed: 11/12/2022] Open
Abstract
We present the generalized mean-field and pairwise models for non-Markovian epidemics on networks with arbitrary recovery time distributions. First we consider a hyperbolic partial differential equation (PDE) system, where the population of infective nodes and links are structured by age since infection. We show that the PDE system can be reduced to a system of integro-differential equations, which is analysed analytically and numerically. We investigate the asymptotic behaviour of the generalized model and provide an implicit analytical expression involving the final epidemic size and pairwise reproduction number. As an illustration of the applicability of the general model, we recover known results for the exponentially distributed and fixed recovery time cases. For gamma- and uniformly distributed infectious periods, new pairwise models are derived. Theoretical findings are confirmed by comparing results from the new pairwise model and explicit stochastic network simulation. A major benefit of the generalized pairwise model lies in approximating the time evolution of the epidemic.
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Affiliation(s)
- G Röst
- Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged 6720, Hungary.,Mathematical Institute, University of Oxford, Oxford, UK
| | - Z Vizi
- Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged 6720, Hungary
| | - I Z Kiss
- School of Mathematical and Physical Sciences, Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK
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36
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Bick C, Sebek M, Kiss IZ. Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions. Phys Rev Lett 2017; 119:168301. [PMID: 29099217 DOI: 10.1103/physrevlett.119.168301] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2017] [Indexed: 05/18/2023]
Abstract
We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on a delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model-based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge chimera dynamics in phase models and real-world oscillator networks.
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Affiliation(s)
- Christian Bick
- Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OX2 6GG Oxford , United Kingdom
- Centre for Systems Dynamics and Control and Department of Mathematics, University of Exeter, EX4 4QF Exeter, United Kingdom
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
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37
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Ferreira MT, Follmann R, Domingues MO, Macau EEN, Kiss IZ. Experimental phase synchronization detection in non-phase coherent chaotic systems by using the discrete complex wavelet approach. Chaos 2017; 27:083122. [PMID: 28863491 DOI: 10.1063/1.4999908] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Phase synchronization may emerge from mutually interacting non-linear oscillators, even under weak coupling, when phase differences are bounded, while amplitudes remain uncorrelated. However, the detection of this phenomenon can be a challenging problem to tackle. In this work, we apply the Discrete Complex Wavelet Approach (DCWA) for phase assignment, considering signals from coupled chaotic systems and experimental data. The DCWA is based on the Dual-Tree Complex Wavelet Transform (DT-CWT), which is a discrete transformation. Due to its multi-scale properties in the context of phase characterization, it is possible to obtain very good results from scalar time series, even with non-phase-coherent chaotic systems without state space reconstruction or pre-processing. The method correctly predicts the phase synchronization for a chemical experiment with three locally coupled, non-phase-coherent chaotic processes. The impact of different time-scales is demonstrated on the synchronization process that outlines the advantages of DCWA for analysis of experimental data.
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Affiliation(s)
- Maria Teodora Ferreira
- Associated Laboratory for Computing and Applied Mathematics (LAC), Brazilian National Institute for Space Research (INPE), São José dos Campos 12227-010, Brazil
| | - Rosangela Follmann
- Associated Laboratory for Computing and Applied Mathematics (LAC), Brazilian National Institute for Space Research (INPE), São José dos Campos 12227-010, Brazil
| | - Margarete O Domingues
- Associated Laboratory for Computing and Applied Mathematics (LAC), Brazilian National Institute for Space Research (INPE), São José dos Campos 12227-010, Brazil
| | - Elbert E N Macau
- Associated Laboratory for Computing and Applied Mathematics (LAC), Brazilian National Institute for Space Research (INPE), São José dos Campos 12227-010, Brazil
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
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38
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Zou W, Sebek M, Kiss IZ, Kurths J. Revival of oscillations from deaths in diffusively coupled nonlinear systems: Theory and experiment. Chaos 2017; 27:061101. [PMID: 28679221 DOI: 10.1063/1.4984927] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching phenomena in coupled nonlinear systems. As a reverse issue of AD and OD, revival of oscillations from deaths attracts an increasing attention recently. In this paper, we clearly disclose that a time delay in the self-feedback component of the coupling destabilizes not only AD but also OD, and even the AD to OD transition in paradigmatic models of coupled Stuart-Landau oscillators under diverse death configurations. Using a rigorous analysis, the effectiveness of this self-feedback delay in revoking AD is theoretically proved to be valid in an arbitrary network of coupled Stuart-Landau oscillators with generally distributed propagation delays. Moreover, the role of self-feedback delay in reviving oscillations from AD is experimentally verified in two delay-coupled electrochemical reactions.
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Affiliation(s)
- Wei Zou
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany
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39
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Kouvaris NE, Sebek M, Iribarne A, Díaz-Guilera A, Kiss IZ. Stationary patterns in star networks of bistable units: Theory and application to chemical reactions. Phys Rev E 2017; 95:042203. [PMID: 28505836 DOI: 10.1103/physreve.95.042203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2017] [Indexed: 06/07/2023]
Abstract
We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the subsequent spreading, pinning, or retraction of the activations; such analysis enables the characterization of the formation of stationary patterns of localized activity. The results are interpreted with a theoretical analysis of a simplified bistable reaction-diffusion model. Weak coupling results in trivial pinned states where the activation cannot propagate. At strong coupling, a uniform state is expected with active or inactive elements at small or large degree networks, respectively. A nontrivial stationary spatial pattern, corresponding to an activation pinning, is predicted to occur at an intermediate number of peripheral elements and at intermediate coupling strengths, where the central activation of the network is pinned, but the peripheral activation propagates toward the center. The results are confirmed in experiments with star networks of bistable electrochemical reactions. The experiments confirm the existence of the stationary spatial patterns and the dependence of coupling strength on the number of peripheral elements for transitions between pinned and retreating or spreading fronts in forced network configurations (where the central or periphery elements are forced to maintain their states).
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Affiliation(s)
- Nikos E Kouvaris
- Center for Brain and Cognition, Universitat Pompeu Fabra, E-08005 Barcelona, Spain
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Ramon Trias Fargas, 25-27, E-08005 Barcelona, Spain
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - Albert Iribarne
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain
| | - Albert Díaz-Guilera
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, E-08007 Barcelona, Spain
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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40
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Abstract
We introduce dual kinetic chronoamperometry, in which reciprocal relations are established between the kinetic curves of electrochemical reactions that start from symmetrical initial conditions. We have performed numerical and experimental studies in which the kinetic curves of the electron-transfer processes are analyzed for a reversible first order reaction. Experimental tests were done with the ferrocyanide/ferricyanide system in which the concentrations of each component could be measured separately using the platinum disk/gold ring electrode. It is shown that the proper ratio of the transient kinetic curves obtained from cathodic and anodic mass transfer limited regions give thermodynamic time invariances related to the reaction quotient of the bulk concentrations. Therefore, thermodynamic time invariances can be observed at any time using the dual kinetic curves for reversible reactions. The technique provides a unique possibility to extract the non-steady state trajectory starting from one initial condition based only on the equilibrium constant and the trajectory which starts from the symmetrical initial condition. The results could impact battery technology by predicting the concentrations and currents of the underlying non-steady state processes in a wide domain from thermodynamic principles and limited kinetic information.
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Affiliation(s)
- Michael J. Hankins
- Department of Chemistry, Saint Louis University, Laclede Av., St. Louis, MO, United States of America
| | - Gregory S. Yablonsky
- Parks College of Engineering, Aviation and Technology, Saint Louis University, Lindell Blvd, St. Louis, MO, United States of America
| | - István Z. Kiss
- Department of Chemistry, Saint Louis University, Laclede Av., St. Louis, MO, United States of America
- * E-mail:
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41
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Kouvaris NE, Sebek M, Mikhailov AS, Kiss IZ. Self-Organized Stationary Patterns in Networks of Bistable Chemical Reactions. Angew Chem Int Ed Engl 2016; 55:13267-13270. [DOI: 10.1002/anie.201607030] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2016] [Indexed: 12/12/2022]
Affiliation(s)
- Nikos E. Kouvaris
- Department of Physics; University of Barcelona; Martí i Franquès 1 08028 Barcelona Spain
| | - Michael Sebek
- Department of Chemistry; Saint Louis University; 3501 Laclede Avenue St. Louis Missouri 63103 USA
| | - Alexander S. Mikhailov
- Department of Physical Chemistry; Fritz Haber Institute of the Max Planck Society; Faradayweg 4-6 14195 Berlin Germany
| | - István Z. Kiss
- Department of Chemistry; Saint Louis University; 3501 Laclede Avenue St. Louis Missouri 63103 USA
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42
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Affiliation(s)
- Nikos E. Kouvaris
- Department of Physics; University of Barcelona; Martí i Franquès 1 08028 Barcelona Spain
| | - Michael Sebek
- Department of Chemistry; Saint Louis University; 3501 Laclede Avenue St. Louis Missouri 63103 USA
| | - Alexander S. Mikhailov
- Department of Physical Chemistry; Fritz Haber Institute of the Max Planck Society; Faradayweg 4-6 14195 Berlin Germany
| | - István Z. Kiss
- Department of Chemistry; Saint Louis University; 3501 Laclede Avenue St. Louis Missouri 63103 USA
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43
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Nagao R, Zou W, Kurths J, Kiss IZ. Restoring oscillatory behavior from amplitude death with anti-phase synchronization patterns in networks of electrochemical oscillations. Chaos 2016; 26:094808. [PMID: 27781452 DOI: 10.1063/1.4954040] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The dynamical behavior of delay-coupled networks of electrochemical reactions is investigated to explore the formation of amplitude death (AD) and the synchronization states in a parameter region around the amplitude death region. It is shown that difference coupling with odd and even numbered ring and random networks can produce the AD phenomenon. Furthermore, this AD can be restored by changing the coupling type from difference to direct coupling. The restored oscillations tend to create synchronization patterns in which neighboring elements are in nearly anti-phase configuration. The ring networks produce frozen and rotating phase waves, while the random network exhibits a complex synchronization pattern with interwoven frozen and propagating phase waves. The experimental results are interpreted with a coupled Stuart-Landau oscillator model. The experimental and theoretical results reveal that AD behavior is a robust feature of delayed coupled networks of chemical units; if an oscillatory behavior is required again, even a small amount of direct coupling could be sufficient to restore the oscillations. The restored nearly anti-phase oscillatory patterns, which, to a certain extent, reflect the symmetry of the network, represent an effective means to overcome the AD phenomenon.
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Affiliation(s)
- Raphael Nagao
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - Wei Zou
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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44
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Sherborne N, Blyuss KB, Kiss IZ. Compact pairwise models for epidemics with multiple infectious stages on degree heterogeneous and clustered networks. J Theor Biol 2016; 407:387-400. [PMID: 27423527 DOI: 10.1016/j.jtbi.2016.07.015] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2016] [Revised: 05/28/2016] [Accepted: 07/10/2016] [Indexed: 12/19/2022]
Abstract
This paper presents a compact pairwise model describing the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian models with exponentially distributed infectious period and epidemics with a constant infectious period. We show how the compact approach leads to a system of equations whose size is independent of the range of node degrees, thus significantly reducing the complexity of the model. Network clustering is incorporated into the model to provide a more accurate representation of realistic contact networks, and the accuracy of proposed closures is analysed for different levels of clustering and number of infection stages. Our results support recent findings that standard closure techniques are likely to perform better when the infectious period is constant.
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Affiliation(s)
- N Sherborne
- Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK
| | - K B Blyuss
- Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK.
| | - I Z Kiss
- Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK
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45
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Abstract
The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information. Organizing and manipulating dynamic processes is important to understand and influence many natural phenomena. Here, the authors present a method to design entrainment signals that create stable phase patterns in heterogeneous nonlinear oscillators, and verify it in electrochemical reactions.
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Affiliation(s)
- Anatoly Zlotnik
- Center for Nonlinear Studies, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Raphael Nagao
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St Louis, Missouri 63103, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St Louis, Missouri 63103, USA
| | - Jr-Shin Li
- Department of Electrical and Systems Engineering, Washington University in St Louis, CB 1042, 1 Brookings Drive, St Louis, Missouri 63130, USA
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46
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Sebek M, Tönjes R, Kiss IZ. Complex Rotating Waves and Long Transients in a Ring Network of Electrochemical Oscillators with Sparse Random Cross-Connections. Phys Rev Lett 2016; 116:068701. [PMID: 26919024 DOI: 10.1103/physrevlett.116.068701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2015] [Indexed: 06/05/2023]
Abstract
We perform experiments and phase model simulations with a ring network of oscillatory electrochemical reactions to explore the effect of random connections and nonisochronicity of the interactions on the pattern formation. A few additional links facilitate the emergence of the fully synchronized state. With larger nonisochronicity, complex rotating waves or persistent irregular phase dynamics can derail the convergence to global synchronization. The observed long transients of irregular phase dynamics exemplify the possibility of a sudden onset of hypersynchronous behavior without any external stimulus or network reorganization.
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Affiliation(s)
- Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - Ralf Tönjes
- Institute of Physics and Astronomy, Potsdam University, 14476 Potsdam-Golm, Germany
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
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Zou W, Senthilkumar DV, Nagao R, Kiss IZ, Tang Y, Koseska A, Duan J, Kurths J. Restoration of rhythmicity in diffusively coupled dynamical networks. Nat Commun 2015; 6:7709. [PMID: 26173555 PMCID: PMC4518287 DOI: 10.1038/ncomms8709] [Citation(s) in RCA: 120] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2015] [Accepted: 06/01/2015] [Indexed: 12/18/2022] Open
Abstract
Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.
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Affiliation(s)
- Wei Zou
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
- Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
- Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany
| | - D. V. Senthilkumar
- Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany
- Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613401, India
| | - Raphael Nagao
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, Missouri 63103, USA
| | - István Z. Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, Missouri 63103, USA
| | - Yang Tang
- Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany
- The Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
| | - Aneta Koseska
- Department of Systemic Cell Biology, Max Planck Institute of Molecular Physiology, Dortmund D-44227, Germany
- Research Centre for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Skopje, Macedonia
| | - Jinqiao Duan
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
- Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany
- Institute of Physics, Humboldt University Berlin, D-12489 Berlin, Germany
- Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX, UK
- Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia
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48
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Nagy T, Verner E, Gáspár V, Kori H, Kiss IZ. Delayed feedback induced multirhythmicity in the oscillatory electrodissolution of copper. Chaos 2015; 25:064608. [PMID: 26117133 DOI: 10.1063/1.4921694] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Occurrence of bi- and trirhythmicities (coexistence of two or three stable limit cycles, respectively, with distinctly different periods) has been studied experimentally by applying delayed feedback control to the copper-phosphoric acid electrochemical system oscillating close to a Hopf bifurcation point under potentiostatic condition. The oscillating electrode potential is delayed by τ and the difference between the present and delayed values is fed back to the circuit potential with a feedback gain K. The experiments were performed by determining the period of current oscillations T as a function of (both increasing and decreasing) τ at several fixed values of K. With small delay times, the period exhibits a sinusoidal type dependence on τ. However, with relatively large delays (typically τ ≫ T) for each feedback gain K, there exists a critical delay τcrit above which birhythmicity emerges. The experiments show that for weak feedback, Kτcrit is approximately constant. At very large delays, the dynamics becomes even more complex, and trirhythmicity could be observed. Results of numerical simulations based on a general kinetic model for metal electrodissolution were consistent with the experimental observations. The experimental and numerical results are also interpreted by using a phase model; the model parameters can be obtained from experimental data measured at small delay times. Analytical solutions to the phase model quantitatively predict the parameter regions for the appearance of birhythmicity in the experiments, and explain the almost constant value of Kτcrit for weak feedback.
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Affiliation(s)
- Timea Nagy
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - Erika Verner
- Department of Physical Chemistry, University of Debrecen, Egyetem tér 1, 4032 Debrecen, Hungary
| | - Vilmos Gáspár
- Department of Physical Chemistry, University of Debrecen, Egyetem tér 1, 4032 Debrecen, Hungary
| | - Hiroshi Kori
- Department of Information Sciences, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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Kiss IZ, Pojman JA. Introduction to Focus Issue: Oscillations and Dynamic Instabilities in Chemical Systems: Dedicated to Irving R. Epstein on occasion of his 70th birthday. Chaos 2015; 25:064201. [PMID: 26117111 DOI: 10.1063/1.4922594] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Affiliation(s)
- István Z Kiss
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
| | - John A Pojman
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, USA
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Wickramasinghe M, Kiss IZ. Spatially organized partial synchronization through the chimera mechanism in a network of electrochemical reactions. Phys Chem Chem Phys 2015; 16:18360-9. [PMID: 25069401 DOI: 10.1039/c4cp02249a] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
Detailed experimental and numerical results are presented about the pattern formation mechanism of spatially organized partially synchronized states in a networked chemical system with oscillatory metal dissolution. Numerical simulations of the reaction system are used to identify experimental conditions (heterogeneity, network topology, and coupling time-scale) under which the chemical reactions, which take place in a network, are split into coexisting coherent and incoherent domains through the chimera mechanism. Experiments are carried out with a network of twenty electrodes arranged in a ring with seven nearest neighbor couplings in both directions along the ring. The patterns are characterized by analyzing the oscillation frequencies and entrainments to the mean field of the phases of oscillations. The chimera state forms from two domains of elements: the chimera core in which the elements have identical frequencies and are entrained to their corresponding mean field and the chimera shell where the elements exhibit desynchrony with each other and the mean field. The experiments point out the importance of low level of heterogeneities (e.g., surface conditions) and optimal level of coupling strength and time-scale as necessary components for the realization of the chimera state. For systems with large heterogeneities, a 'remnant' chimera state is identified where the pattern is strongly affected by the presence of frequency clusters. The exploration of dynamical features with networked reactions could open up ways for identification of novel types of patterns that cannot be observed with reaction diffusion systems (with localized interactions) or with reactions under global constraints, coupling, or feedback.
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Affiliation(s)
- Mahesh Wickramasinghe
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA.
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