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Chu YM, Alzahrani T, Rashid S, Rashidah W, Ur Rehman S, Alkhatib M. An advanced approach for the electrical responses of discrete fractional-order biophysical neural network models and their dynamical responses. Sci Rep 2023; 13:18180. [PMID: 37875469 PMCID: PMC10598013 DOI: 10.1038/s41598-023-45227-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2023] [Accepted: 10/17/2023] [Indexed: 10/26/2023] Open
Abstract
The multiple activities of neurons frequently generate several spiking-bursting variations observed within the neurological mechanism. We show that a discrete fractional-order activated nerve cell framework incorporating a Caputo-type fractional difference operator can be used to investigate the impacts of complex interactions on the surge-empowering capabilities noticed within our findings. The relevance of this expansion is based on the model's structure as well as the commensurate and incommensurate fractional-orders, which take kernel and inherited characteristics into account. We begin by providing data regarding the fluctuations in electronic operations using the fractional exponent. We investigate two-dimensional Morris-Lecar neuronal cell frameworks via spiked and saturated attributes, as well as mixed-mode oscillations and mixed-mode bursting oscillations of a decoupled fractional-order neuronal cell. The investigation proceeds by using a three-dimensional slow-fast Morris-Lecar simulation within the fractional context. The proposed method determines a method for describing multiple parallels within fractional and integer-order behaviour. We examine distinctive attribute environments where inactive status develops in detached neural networks using stability and bifurcation assessment. We demonstrate features that are in accordance with the analysis's findings. The Erdös-Rényi connection of asynchronization transformed neural networks (periodic and actionable) is subsequently assembled and paired via membranes that are under pressure. It is capable of generating multifaceted launching processes in which dormant neural networks begin to come under scrutiny. Additionally, we demonstrated that boosting connections can cause classification synchronization, allowing network devices to activate in conjunction in the future. We construct a reduced-order simulation constructed around clustering synchronisation that may represent the operations that comprise the whole system. Our findings indicate the influence of fractional-order is dependent on connections between neurons and the system's stored evidence. Moreover, the processes capture the consequences of fractional derivatives on surge regularity modification and enhance delays that happen across numerous time frames in neural processing.
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Affiliation(s)
- Yu-Ming Chu
- School of Science, Hunan City University, Yiyang, 413000, People's Republic of China
| | - Taher Alzahrani
- Information Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
| | - Saima Rashid
- Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan.
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, 1401, Lebanon.
| | - Waleed Rashidah
- Information Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
| | - Shafiq Ur Rehman
- Information Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
| | - Mohammad Alkhatib
- Computer Science Department, College of Computer and information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
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Sharma SK, Mondal A, Kaslik E, Hens C, Antonopoulos CG. Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems. Sci Rep 2023; 13:8215. [PMID: 37217514 DOI: 10.1038/s41598-023-34807-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 05/08/2023] [Indexed: 05/24/2023] Open
Abstract
The diverse excitabilities of cells often produce various spiking-bursting oscillations that are found in the neural system. We establish the ability of a fractional-order excitable neuron model with Caputo's fractional derivative to analyze the effects of its dynamics on the spike train features observed in our results. The significance of this generalization relies on a theoretical framework of the model in which memory and hereditary properties are considered. Employing the fractional exponent, we first provide information about the variations in electrical activities. We deal with the 2D class I and class II excitable Morris-Lecar (M-L) neuron models that show the alternation of spiking and bursting features including MMOs & MMBOs of an uncoupled fractional-order neuron. We then extend the study with the 3D slow-fast M-L model in the fractional domain. The considered approach establishes a way to describe various characteristics similarities between fractional-order and classical integer-order dynamics. Using the stability and bifurcation analysis, we discuss different parameter spaces where the quiescent state emerges in uncoupled neurons. We show the characteristics consistent with the analytical results. Next, the Erdös-Rényi network of desynchronized mixed neurons (oscillatory and excitable) is constructed that is coupled through membrane voltage. It can generate complex firing activities where quiescent neurons start to fire. Furthermore, we have shown that increasing coupling can create cluster synchronization, and eventually it can enable the network to fire in unison. Based on cluster synchronization, we develop a reduced-order model which can capture the activities of the entire network. Our results reveal that the effect of fractional-order depends on the synaptic connectivity and the memory trace of the system. Additionally, the dynamics captures spike frequency adaptation and spike latency that occur over multiple timescales as the effects of fractional derivative, which has been observed in neural computation.
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Affiliation(s)
- Sanjeev K Sharma
- Department of Mathematics, VIT-AP University, Amaravati, 522237, Andhra Pradesh, India
| | - Argha Mondal
- Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, 723104, West Bengal, India.
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, UK.
| | - Eva Kaslik
- Department of Mathematics and Computer Science, West University of Timisoara, Timisoara, Romania.
- Institute for Advanced Environmental Research, West University of Timisoara, Timisoara, Romania.
| | | | - Chris G Antonopoulos
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, UK.
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Barać U, Perc M, Gosak M. Determinants of collective failure in excitable networks. CHAOS (WOODBURY, N.Y.) 2023; 33:043120. [PMID: 37097938 DOI: 10.1063/5.0149578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2023] [Accepted: 03/27/2023] [Indexed: 06/19/2023]
Abstract
We study collective failures in biologically realistic networks that consist of coupled excitable units. The networks have broad-scale degree distribution, high modularity, and small-world properties, while the excitable dynamics is determined by the paradigmatic FitzHugh-Nagumo model. We consider different coupling strengths, bifurcation distances, and various aging scenarios as potential culprits of collective failure. We find that for intermediate coupling strengths, the network remains globally active the longest if the high-degree nodes are first targets for inactivation. This agrees well with previously published results, which showed that oscillatory networks can be highly fragile to the targeted inactivation of low-degree nodes, especially under weak coupling. However, we also show that the most efficient strategy to enact collective failure does not only non-monotonically depend on the coupling strength, but it also depends on the distance from the bifurcation point to the oscillatory behavior of individual excitable units. Altogether, we provide a comprehensive account of determinants of collective failure in excitable networks, and we hope this will prove useful for better understanding breakdowns in systems that are subject to such dynamics.
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Affiliation(s)
- Uroš Barać
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
| | - Matjaž Perc
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
- Alma Mater Europaea, Slovenska ulica 17, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, 40447 Taichung, Taiwan
- Complexity Science Hub Vienna, Josefstädterstrasse 39, 1080 Vienna, Austria
- Department of Physics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, 02447 Seoul, Republic of Korea
| | - Marko Gosak
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
- Alma Mater Europaea, Slovenska ulica 17, 2000 Maribor, Slovenia
- Institute of Physiology, Faculty of Medicine, University of Maribor, Taborska ulica 8, 2000 Maribor, Slovenia
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Sharma A, Rakshit B. Enhancement of dynamical robustness in a mean-field coupled network through self-feedback delay. CHAOS (WOODBURY, N.Y.) 2021; 31:013114. [PMID: 33754750 DOI: 10.1063/5.0015821] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2020] [Accepted: 12/16/2020] [Indexed: 06/12/2023]
Abstract
The network of self-sustained oscillators plays an important role in exploring complex phenomena in many areas of science and technology. The aging of an oscillator is referred to as turning non-oscillatory due to some local perturbations that might have adverse effects in macroscopic dynamical activities of a network. In this article, we propose an efficient technique to enhance the dynamical activities for a network of coupled oscillators experiencing aging transition. In particular, we present a control mechanism based on delayed negative self-feedback, which can effectively enhance dynamical robustness in a mean-field coupled network of active and inactive oscillators. Even for a small value of delay, robustness gets enhanced to a significant level. In our proposed scheme, the enhancing effect is more pronounced for strong coupling. To our surprise even if all the oscillators perturbed to equilibrium mode were delayed negative self-feedback is able to restore oscillatory activities in the network for strong coupling strength. We demonstrate that our proposed mechanism is independent of coupling topology. For a globally coupled network, we provide numerical and analytical treatment to verify our claim. To show that our scheme is independent of network topology, we also provide numerical results for the local mean-field coupled complex network. Also, for global coupling to establish the generality of our scheme, we validate our results for both Stuart-Landau limit cycle oscillators and chaotic Rössler oscillators.
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Affiliation(s)
- Amit Sharma
- Department of Physics, Central University of Rajasthan, Ajmer 305 817, India
| | - Biswambhar Rakshit
- Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641 112, India
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Rakshit B, Rajendrakumar N, Balaram B. Abnormal route to aging transition in a network of coupled oscillators. CHAOS (WOODBURY, N.Y.) 2020; 30:101101. [PMID: 33138470 DOI: 10.1063/5.0022499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Accepted: 09/17/2020] [Indexed: 06/11/2023]
Abstract
In this article, we investigate the dynamical robustness in a network of Van der Pol oscillators. In particular, we consider a network of diffusively coupled Van der Pol oscillators to explore the aging transition phenomena. Our investigation reveals that the route to aging transition in a network of Van der Pol oscillator is different from that of typical sinusoidal oscillators such as Stuart-Landau oscillators. Unlike sinusoidal oscillators, the order parameter does not follow smooth second-order phase transition. Rather, we observe an abnormal phase transition of the order parameter due to the sudden appearance of unbounded trajectories at a critical point. We provide detailed bifurcation analysis of such an abnormal phase transition. We show that the boundary crisis of a limit-cycle oscillator is at the helm of such an unusual discontinuous path of aging transition.
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Affiliation(s)
- Biswambhar Rakshit
- Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641 112, India
| | - Niveditha Rajendrakumar
- Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands
| | - Bipin Balaram
- Department of Mechanical Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641 112, India
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Ghosh S, Mondal A, Ji P, Mishra A, Dana SK, Antonopoulos CG, Hens C. Emergence of Mixed Mode Oscillations in Random Networks of Diverse Excitable Neurons: The Role of Neighbors and Electrical Coupling. Front Comput Neurosci 2020; 14:49. [PMID: 32581757 PMCID: PMC7294985 DOI: 10.3389/fncom.2020.00049] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 05/04/2020] [Indexed: 11/21/2022] Open
Abstract
In this paper, we focus on the emergence of diverse neuronal oscillations arising in a mixed population of neurons with different excitability properties. These properties produce mixed mode oscillations (MMOs) characterized by the combination of large amplitudes and alternate subthreshold or small amplitude oscillations. Considering the biophysically plausible, Izhikevich neuron model, we demonstrate that various MMOs, including MMBOs (mixed mode bursting oscillations) and synchronized tonic spiking appear in a randomly connected network of neurons, where a fraction of them is in a quiescent (silent) state and the rest in self-oscillatory (firing) states. We show that MMOs and other patterns of neural activity depend on the number of oscillatory neighbors of quiescent nodes and on electrical coupling strengths. Our results are verified by constructing a reduced-order network model and supported by systematic bifurcation diagrams as well as for a small-world network. Our results suggest that, for weak couplings, MMOs appear due to the de-synchronization of a large number of quiescent neurons in the networks. The quiescent neurons together with the firing neurons produce high frequency oscillations and bursting activity. The overarching goal is to uncover a favorable network architecture and suitable parameter spaces where Izhikevich model neurons generate diverse responses ranging from MMOs to tonic spiking.
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Affiliation(s)
- Subrata Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India
| | - Argha Mondal
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India
| | - Peng Ji
- The Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
| | - Arindam Mishra
- Department of Mathematics, Centre for Mathematical Biology and Ecology, Jadavpur University, Kolkata, India
| | - Syamal K Dana
- Department of Mathematics, Centre for Mathematical Biology and Ecology, Jadavpur University, Kolkata, India.,Division of Dynamics, Faculty of Mechanical Engineering, Lodz University of Technology, Lodz, Poland
| | - Chris G Antonopoulos
- Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India
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7
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Sun Z, Liu Y, Liu K, Yang X, Xu W. Aging transition in mixed active and inactive fractional-order oscillators. CHAOS (WOODBURY, N.Y.) 2019; 29:103150. [PMID: 31675845 DOI: 10.1063/1.5114998] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Accepted: 10/09/2019] [Indexed: 06/10/2023]
Abstract
Recently, a large number of studies have concentrated on aging transition, but they have so far been restricted to coupled integer-order oscillators. Here, we report the first study of aging transition in mixed active and inactive fractional-order oscillators. It has been demonstrated that while the heterogeneity is caused by the distance parameter, both the coupling strength and the fractional-order derivative can modulate the critical ratio at which aging transition occurs. In addition, a small fractional-order derivative may ruin the ability of oscillation and, thus, reduce the critical ratio in globally coupled fractional-order Stuart-Landau oscillators. Remarkably, the larger the natural frequency is the more easily the aging transition occurs in coupled fractional-order oscillators. Further studies have shown that, being diverse from an integer-order Stuart-Landau oscillator, the natural frequency may induce a Hopf bifurcation in a fractional-order Stuart-Landau oscillator, accordingly, introducing a new heterogeneity in the coupled fractional-order Stuart-Landau oscillators. Therein, a counterintuitive phenomenon has been found that the critical ratio depends unmonotonously on the coupling strength, which implies that the coupled fractional-order Stuart-Landau oscillators possess the weakest robustness of oscillation at a certain level of coupling strength.
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Affiliation(s)
- Zhongkui Sun
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China
| | - Yuanyuan Liu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China
| | - Ke Liu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China
| | - Xiaoli Yang
- College of Mathematics and Information Science, Shaan'xi Normal University, Xi'an 710062, People's Republic of China
| | - Wei Xu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China
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8
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Kundu S, Majhi S, Sasmal SK, Ghosh D, Rakshit B. Survivability of a metapopulation under local extinctions. Phys Rev E 2017; 96:062212. [PMID: 29347456 DOI: 10.1103/physreve.96.062212] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2017] [Indexed: 06/07/2023]
Abstract
A metapopulation structure in landscape ecology comprises a group of interacting spatially separated subpopulations or patches of the same species that may experience several local extinctions. This makes the investigation of survivability (in the form of global oscillation) of a metapopulation on top of diverse dispersal topologies extremely crucial. However, among various dispersal topologies in ecological networks, which one can provide higher metapopulation survivability under local extinction is still not well explored. In this article, we scrutinize the robustness of an ecological network consisting of prey-predator patches having Holling type I functional response, against progressively extinct population patches. We present a comprehensive study on this while considering global, small-world, and scale-free dispersal of the subpopulations. Furthermore, we extend our work in enhancing survivability in the form of sustained global oscillation by introducing asymmetries in the dispersal rates of the considered species. Our findings affirm that the asynchrony among the patches plays an important role in the survivability of a metapopulation. In order to demonstrate the model independence of the observed phenomenon, we perform a similar analysis for patches exhibiting Holling type II functional response. On the grounds of the obtained results, our work is expected to provide a better perception of the influence of dispersal arrangements on the global survivability of ecological networks.
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Affiliation(s)
- Srilena Kundu
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Sourav Kumar Sasmal
- Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Biswambhar Rakshit
- Department of Mathematics, Amrita School of Engineering-Coimbatore Amrita Vishwa Vidyapeetham, India
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9
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Yuan T, Tanaka G. Robustness of coupled oscillator networks with heterogeneous natural frequencies. CHAOS (WOODBURY, N.Y.) 2017; 27:123105. [PMID: 29289041 DOI: 10.1063/1.4991742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2017] [Accepted: 11/23/2017] [Indexed: 06/07/2023]
Abstract
Robustness of coupled oscillator networks against local degradation of oscillators has been intensively studied in this decade. The oscillation behavior on the whole network is typically reduced with an increase in the fraction of degraded (inactive) oscillators. The critical fraction of inactive oscillators, at which a transition from an oscillatory to a quiescent state occurs, has been used as a measure for the network robustness. The larger (smaller) this measure is, the more robust (fragile) the oscillatory behavior on the network is. Most previous studies have used oscillators with identical natural frequencies, for which the oscillators are necessarily synchronized and thereby the analysis is simple. In contrast, we focus on the effect of heterogeneity in the natural frequencies on the network robustness. First, we analytically derive the robustness measure for the coupled oscillator models with heterogeneous natural frequencies under some conditions. Then, we show that increasing the heterogeneity in natural frequencies makes the network fragile. Moreover, we discuss the optimal parameter condition to maximize the network robustness.
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Affiliation(s)
- Tianyu Yuan
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - Gouhei Tanaka
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
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10
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Rahman B, Blyuss KB, Kyrychko YN. Aging transition in systems of oscillators with global distributed-delay coupling. Phys Rev E 2017; 96:032203. [PMID: 29347035 DOI: 10.1103/physreve.96.032203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2016] [Indexed: 06/07/2023]
Abstract
We consider a globally coupled network of active (oscillatory) and inactive (nonoscillatory) oscillators with distributed-delay coupling. Conditions for aging transition, associated with suppression of oscillations, are derived for uniform and gamma delay distributions in terms of coupling parameters and the proportion of inactive oscillators. The results suggest that for the uniform distribution increasing the width of distribution for the same mean delay allows aging transition to happen for a smaller coupling strength and a smaller proportion of inactive elements. For gamma distribution with sufficiently large mean time delay, it may be possible to achieve aging transition for an arbitrary proportion of inactive oscillators, as long as the coupling strength lies in a certain range.
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Affiliation(s)
- B Rahman
- Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, England, United Kingdom
| | - K B Blyuss
- Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, England, United Kingdom
| | - Y N Kyrychko
- Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, England, United Kingdom
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Trinh HC, Kwon YK. Edge-based sensitivity analysis of signaling networks by using Boolean dynamics. Bioinformatics 2017; 32:i763-i771. [PMID: 27587699 DOI: 10.1093/bioinformatics/btw464] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
MOTIVATION Biological networks are composed of molecular components and their interactions represented by nodes and edges, respectively, in a graph model. Based on this model, there were many studies with respect to effects of node-based mutations on the network dynamics, whereas little attention was paid to edgetic mutations so far. RESULTS In this paper, we defined an edgetic sensitivity measure that quantifies how likely a converging attractor is changed by edge-removal mutations in a Boolean network model. Through extensive simulations based on that measure, we found interesting properties of highly sensitive edges in both random and real signaling networks. First, the sensitive edges in random networks tend to link two end nodes both of which are susceptible to node-knockout mutations. Interestingly, it was analogous to an observation that the sensitive edges in human signaling networks are likely to connect drug-target genes. We further observed that the edgetic sensitivity predicted drug-targets better than the node-based sensitivity. In addition, the sensitive edges showed distinguished structural characteristics such as a lower connectivity, more involving feedback loops and a higher betweenness. Moreover, their gene-ontology enrichments were clearly different from the other edges. We also observed that genes incident to the highly sensitive interactions are more central by forming a considerably large connected component in human signaling networks. Finally, we validated our approach by showing that most sensitive interactions are promising edgetic drug-targets in p53 cancer and T-cell apoptosis networks. Taken together, the edgetic sensitivity is valuable to understand the complex dynamics of signaling networks. CONTACT kwonyk@ulsan.ac.kr SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Hung-Cuong Trinh
- School of Electrical Engineering, University of Ulsan, 93 Daehak-Ro, Ulsan, 44610 Nam -Gu, Republic of Korea
| | - Yung-Keun Kwon
- School of Electrical Engineering, University of Ulsan, 93 Daehak-Ro, Ulsan, 44610 Nam -Gu, Republic of Korea
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12
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Yuan T, Aihara K, Tanaka G. Robustness and fragility in coupled oscillator networks under targeted attacks. Phys Rev E 2017; 95:012315. [PMID: 28208319 DOI: 10.1103/physreve.95.012315] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2016] [Indexed: 06/06/2023]
Abstract
The dynamical tolerance of coupled oscillator networks against local failures is studied. As the fraction of failed oscillator nodes gradually increases, the mean oscillation amplitude in the entire network decreases and then suddenly vanishes at a critical fraction as a phase transition. This critical fraction, widely used as a measure of the network robustness, was analytically derived for random failures but not for targeted attacks so far. Here we derive the general formula for the critical fraction, which can be applied to both random failures and targeted attacks. We consider the effects of targeting oscillator nodes based on their degrees. First we deal with coupled identical oscillators with homogeneous edge weights. Then our theory is applied to networks with heterogeneous edge weights and to those with nonidentical oscillators. The analytical results are validated by numerical experiments. Our results reveal the key factors governing the robustness and fragility of oscillator networks.
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Affiliation(s)
- Tianyu Yuan
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - Kazuyuki Aihara
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
- Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
| | - Gouhei Tanaka
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
- Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
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