1
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Nag Chowdhury S, Anwar MS, Ghosh D. Cluster formation due to repulsive spanning trees in attractively coupled networks. Phys Rev E 2024; 109:044314. [PMID: 38755838 DOI: 10.1103/physreve.109.044314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2023] [Accepted: 03/22/2024] [Indexed: 05/18/2024]
Abstract
Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological processes. The current literature has investigated cluster synchronization by focusing mostly on the case of attractive coupling among the oscillators. However, the case of two coexisting competing interactions is of practical interest due to their relevance in diverse natural settings, including neuronal networks consisting of excitatory and inhibitory neurons, the coevolving social model with voters of opposite opinions, and ecological plant communities with both facilitation and competition, to name a few. In the present article, we investigate the impact of repulsive spanning trees on cluster formation within a connected network of attractively coupled limit-cycle oscillators. We successfully predict which nodes belong to each cluster and the emergent frustration of the connected networks independent of the particular local dynamics at the network nodes. We also determine local asymptotic stability of the cluster states using an approach based on the formulation of a master stability function. We additionally validate the emergence of solitary states and antisynchronization for some specific choices of spanning trees and networks.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, Davis, California 95616, USA
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Md Sayeed Anwar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
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2
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Vandermeer J, Perfecto I. Combining intransitive and higher-order effects in a coupled oscillator framework: A case study of an ant community. Ecology 2024; 105:e4218. [PMID: 38032663 DOI: 10.1002/ecy.4218] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/27/2023] [Revised: 09/19/2023] [Accepted: 10/20/2023] [Indexed: 12/01/2023]
Abstract
A growing body of literature recognizes that pairwise species interactions are not necessarily an appropriate metaphorical molecule of community ecology. Two examples are intransitive competition and nonlinear higher-order effects. While these two processes have been discussed extensively, the explicit analysis of how the two of them behave when simultaneously part of the same dynamic system has not yet been explored theoretically. A concrete situation exists on coffee farms in Puerto Rico in which three ant species form an intransitive competitive triplet, and that triplet is strongly influenced, nonlinearly, by a fly parasitoid that modifies the competitive ability of one of the species. Using this arrangement as a template, we explore the dynamical consequences with a simple ordinary differential equation (ODE) model. Results are complicated and include alternative periodic and chaotic attractors. The qualitative structures of those complications, however, may be approximately retrieved from the basic natural history of the system.
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Affiliation(s)
- John Vandermeer
- Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, Michigan, USA
- School of Environment and Sustainability, University of Michigan, Ann Arbor, Michigan, USA
| | - Ivette Perfecto
- School of Environment and Sustainability, University of Michigan, Ann Arbor, Michigan, USA
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3
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Lu Y, Wang X, Du C, Wang Y, Geng Y, Shi L, Park J. Understanding the role of neutral species by means of high-order interaction in the rock-paper-scissors dynamics. Phys Rev E 2024; 109:014313. [PMID: 38366519 DOI: 10.1103/physreve.109.014313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 01/05/2024] [Indexed: 02/18/2024]
Abstract
The existence of neutral species carries profound ecological implications that warrant further investigation. In this paper, we study the impact of neutral species on biodiversity in a spatial tritrophic system of cyclic competition, in which the neutral species are identified as the fourth species that may affect the competition process of the other three species under the rock-paper-scissors (RPS) rule. Extensive simulations showed that neutral species can promote coexistence in a high mobility regime within the system. When coexistence occurs, we found that the state can be maintained by two mechanisms: Species can either (i) adhere to traditional RPS rule or (ii) form patches to resist invasion. Our findings might aid in understanding the impact of neutral species on biodiversity in ecosystems.
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Affiliation(s)
- Yikang Lu
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
- Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, 50018 Zaragoza, Spain
| | - Xiaoyue Wang
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
| | - Chunpeng Du
- School of Mathematics, Kunming University, Kunming, 650214, China
| | - Yanan Wang
- Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, 50018 Zaragoza, Spain
- School of Economics and Management, Beihang University, Beijing 100191, China
| | - Yini Geng
- School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
| | - Lei Shi
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
- Interdisciplinary Research Institute of Data Science, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
| | - Junpyo Park
- Department of Applied Mathematics, College of Applied Sciences, Kyung Hee University, Yongin 17104, Republic of Korea
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4
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Chatterjee S, De R, Hens C, Dana SK, Kapitaniak T, Bhattacharyya S. Response of a three-species cyclic ecosystem to a short-lived elevation of death rate. Sci Rep 2023; 13:20740. [PMID: 38007582 PMCID: PMC10676407 DOI: 10.1038/s41598-023-48104-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2023] [Accepted: 11/22/2023] [Indexed: 11/27/2023] Open
Abstract
A balanced ecosystem with coexisting constituent species is often perturbed by different natural events that persist only for a finite duration of time. What becomes important is whether, in the aftermath, the ecosystem recovers its balance or not. Here we study the fate of an ecosystem by monitoring the dynamics of a particular species that encounters a sudden increase in death rate. For exploration of the fate of the species, we use Monte-Carlo simulation on a three-species cyclic rock-paper-scissor model. The density of the affected (by perturbation) species is found to drop exponentially immediately after the pulse is applied. In spite of showing this exponential decay as a short-time behavior, there exists a region in parameter space where this species surprisingly remains as a single survivor, wiping out the other two which had not been directly affected by the perturbation. Numerical simulations using stochastic differential equations of the species give consistency to our results.
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Affiliation(s)
- Sourin Chatterjee
- Department of Mathematics and Statistics, Indian Institute of Science Education and Research, Kolkata, West Bengal, 741246, India
| | - Rina De
- Department of Physics, Raja Rammohun Roy Mahavidyalaya, Radhanagar, Hooghly, 712406, India
| | - Chittaranjan Hens
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad, 500 032, India
- Division of Dynamics, Faculty of Mechanical Engineering, Lodz University of Technology, 90-924, Lodz, Poland
| | - Syamal K Dana
- Division of Dynamics, Faculty of Mechanical Engineering, Lodz University of Technology, 90-924, Lodz, Poland
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata, 700032, India
| | - Tomasz Kapitaniak
- Division of Dynamics, Faculty of Mechanical Engineering, Lodz University of Technology, 90-924, Lodz, Poland
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5
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Dutta S, Mondal A, Kundu P, Khanra P, Pal P, Hens C. Impact of phase lag on synchronization in frustrated Kuramoto model with higher-order interactions. Phys Rev E 2023; 108:034208. [PMID: 37849147 DOI: 10.1103/physreve.108.034208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Accepted: 08/25/2023] [Indexed: 10/19/2023]
Abstract
The study of first order transition (explosive synchronization) in an ensemble (network) of coupled oscillators has been the topic of paramount interest among the researchers for more than one decade. Several frameworks have been proposed to induce explosive synchronization in a network and it has been reported that phase frustration in a network usually suppresses first order transition in the presence of pairwise interactions among the oscillators. However, on the contrary, by considering networks of phase frustrated coupled oscillators in the presence of higher-order interactions (up to 2-simplexes) we show here, under certain conditions, phase frustration can promote explosive synchronization in a network. A low-dimensional model of the network in the thermodynamic limit is derived using the Ott-Antonsen ansatz to explain this surprising result. Analytical treatment of the low-dimensional model, including bifurcation analysis, explains the apparent counter intuitive result quite clearly.
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Affiliation(s)
- Sangita Dutta
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Abhijit Mondal
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Prosenjit Kundu
- Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat 382007, India
| | - Pitambar Khanra
- Department of Mathematics, State University of New York at Buffalo, Buffalo 14260, USA
| | - Pinaki Pal
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Chittaranjan Hens
- Center for Computational Natural Science and Bioinformatics, International Institute of Informational Technology, Gachibowli, Hyderabad 500032, India
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Roy S, Nag Chowdhury S, Kundu S, Sar GK, Banerjee J, Rakshit B, Mali PC, Perc M, Ghosh D. Time delays shape the eco-evolutionary dynamics of cooperation. Sci Rep 2023; 13:14331. [PMID: 37653103 PMCID: PMC10471784 DOI: 10.1038/s41598-023-41519-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2023] [Accepted: 08/28/2023] [Indexed: 09/02/2023] Open
Abstract
We study the intricate interplay between ecological and evolutionary processes through the lens of the prisoner's dilemma game. But while previous studies on cooperation amongst selfish individuals often assume instantaneous interactions, we take into consideration delays to investigate how these might affect the causes underlying prosocial behavior. Through analytical calculations and numerical simulations, we demonstrate that delays can lead to oscillations, and by incorporating also the ecological variable of altruistic free space and the evolutionary strategy of punishment, we explore how these factors impact population and community dynamics. Depending on the parameter values and the initial fraction of each strategy, the studied eco-evolutionary model can mimic a cyclic dominance system and even exhibit chaotic behavior, thereby highlighting the importance of complex dynamics for the effective management and conservation of ecological communities. Our research thus contributes to the broader understanding of group decision-making and the emergence of moral behavior in multidimensional social systems.
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Affiliation(s)
- Sourav Roy
- Department of Mathematics, Jadavpur University, Kolkata, 700032, India
| | - Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, CA, 95616, USA
| | - Srilena Kundu
- Department of Ecology & Evolution, University of Chicago, Chicago, IL, 60637, USA
| | - Gourab Kumar Sar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India
| | - Jeet Banerjee
- BYJU'S, Think & Learn Pvt. Ltd., IBC Knowledge Park, 4/1 Bannerghatta Main Road, Bangalore, 560029, India
| | - Biswambhar Rakshit
- Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, India
| | | | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 404332, Taiwan
- Alma Mater Europaea, Slovenska ulica 17, 2000, Maribor, Slovenia
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080, Vienna, Austria
- Department of Physics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India.
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7
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Dutta S, Kundu P, Khanra P, Hens C, Pal P. Perfect synchronization in complex networks with higher-order interactions. Phys Rev E 2023; 108:024304. [PMID: 37723785 DOI: 10.1103/physreve.108.024304] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 07/11/2023] [Indexed: 09/20/2023]
Abstract
Achieving perfect synchronization in a complex network, specially in the presence of higher-order interactions (HOIs) at a targeted point in the parameter space, is an interesting, yet challenging task. Here we present a theoretical framework to achieve the same under the paradigm of the Sakaguchi-Kuramoto (SK) model. We analytically derive a frequency set to achieve perfect synchrony at some desired point in a complex network of SK oscillators with higher-order interactions. Considering the SK model with HOIs on top of the scale-free, random, and small world networks, we perform extensive numerical simulations to verify the proposed theory. Numerical simulations show that the analytically derived frequency set not only provides stable perfect synchronization in the network at a desired point but also proves to be very effective in achieving a high level of synchronization around it compared to the other choices of frequency sets. The stability and the robustness of the perfect synchronization state of the system are determined using the low-dimensional reduction of the network and by introducing a Gaussian noise around the derived frequency set, respectively.
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Affiliation(s)
- Sangita Dutta
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Prosenjit Kundu
- Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat 382007, India
| | - Pitambar Khanra
- Department of Mathematics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - Chittaranjan Hens
- Center for Computational Natural Science and Bioinformatics, International Institute of Informational Technology, Gachibowli, Hyderabad 500032, India
| | - Pinaki Pal
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
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8
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Jaros P, Ghosh S, Dudkowski D, Dana SK, Kapitaniak T. Higher-order interactions in Kuramoto oscillators with inertia. Phys Rev E 2023; 108:024215. [PMID: 37723775 DOI: 10.1103/physreve.108.024215] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Accepted: 08/01/2023] [Indexed: 09/20/2023]
Abstract
How do higher-order interactions influence the dynamical landscape of a network of the second-order phase oscillators? We address this question using three coupled Kuramoto phase oscillators with inertia under pairwise and higher-order interactions, in search of various collective states, and new states, if any, that show marginal presence or absence under pairwise interactions. We explore this small network for varying phase lag in the coupling and over a range of negative to positive coupling strength of pairwise as well as higher-order or group interactions. In the extended coupling parameter plane of the network we record several well-known states such as synchronization, frequency chimera states, and rotating waves that appear with distinct boundaries. In the parameter space, we also find states generated by the influence of higher-order interactions: The 2+1 antipodal point and the 2+1 phase-locked states. Our results demonstrate the importantance of the choices of the phase lag and the sign of the higher-order coupling strength for the emergent dynamics of the network. We provide analytical support to our numerical results.
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Affiliation(s)
- Patrycja Jaros
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Subrata Ghosh
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
| | - Dawid Dudkowski
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Syamal K Dana
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
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9
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Nag Chowdhury S, Banerjee J, Perc M, Ghosh D. Eco-evolutionary cyclic dominance among predators, prey, and parasites. J Theor Biol 2023; 564:111446. [PMID: 36868345 DOI: 10.1016/j.jtbi.2023.111446] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 02/24/2023] [Accepted: 02/25/2023] [Indexed: 03/05/2023]
Abstract
Predator-prey interactions are one of ecology's central research themes, but with many interdisciplinary implications across the social and natural sciences. Here we consider an often-overlooked species in these interactions, namely parasites. We first show that a simple predator-prey-parasite model, inspired by the classical Lotka-Volterra equations, fails to produce a stable coexistence of all three species, thus failing to provide a biologically realistic outcome. To improve this, we introduce free space as a relevant eco-evolutionary component in a new mathematical model that uses a game-theoretical payoff matrix to describe a more realistic setup. We then show that the consideration of free space stabilizes the dynamics by means of cyclic dominance that emerges between the three species. We determine the parameter regions of coexistence as well as the types of bifurcations leading to it by means of analytical derivations as well as by means of numerical simulations. We conclude that the consideration of free space as a finite resource reveals the limits of biodiversity in predator-prey-parasite interactions, and it may also help us in the determination of factors that promote a healthy biota.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, CA 95616, USA
| | - Jeet Banerjee
- BYJU'S, Think & Learn Pvt. Ltd., IBC Knowledge Park, 4/1 Bannerghatta Main Road, Bangalore 560029, India
| | - Matjaž Perc
- 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, Taichung, Taiwan; Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria; Department of Physics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India.
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10
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Ghosh S, Khanra P, Kundu P, Ji P, Ghosh D, Hens C. Dimension reduction in higher-order contagious phenomena. CHAOS (WOODBURY, N.Y.) 2023; 33:2893033. [PMID: 37229635 DOI: 10.1063/5.0152959] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 05/01/2023] [Indexed: 05/27/2023]
Abstract
We investigate epidemic spreading in a deterministic susceptible-infected-susceptible model on uncorrelated heterogeneous networks with higher-order interactions. We provide a recipe for the construction of one-dimensional reduced model (resilience function) of the N-dimensional susceptible-infected-susceptible dynamics in the presence of higher-order interactions. Utilizing this reduction process, we are able to capture the microscopic and macroscopic behavior of infectious networks. We find that the microscopic state of nodes (fraction of stable healthy individual of each node) inversely scales with their degree, and it becomes diminished due to the presence of higher-order interactions. In this case, we analytically obtain that the macroscopic state of the system (fraction of infectious or healthy population) undergoes abrupt transition. Additionally, we quantify the network's resilience, i.e., how the topological changes affect the stable infected population. Finally, we provide an alternative framework of dimension reduction based on the spectral analysis of the network, which can identify the critical onset of the disease in the presence or absence of higher-order interactions. Both reduction methods can be extended for a large class of dynamical models.
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Affiliation(s)
- Subrata Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Pitambar Khanra
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260, USA
| | - Prosenjit Kundu
- Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat 382007, India
| | - Peng Ji
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China
- Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai 200433, China
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
- International Institute of Information Technology, Hyderabad 500 032, India
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11
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Chatterjee S, Nag Chowdhury S, Ghosh D, Hens C. Erratum: "Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions" [Chaos 32(10), 103122 (2022)]. CHAOS (WOODBURY, N.Y.) 2023; 33:049901. [PMID: 37097931 DOI: 10.1063/5.0150932] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 03/27/2023] [Indexed: 06/19/2023]
Affiliation(s)
- Sourin Chatterjee
- Department of Mathematics and Statistics, Indian Institute of Science Education and Research, Kolkata, West Bengal 741246, India
| | - Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
- Technology Innovation Hub (TIH), IDEAS (Institute of Data Engineering Analytics and Science Foundation) @ Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
- International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
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12
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Gao Z, Ghosh D, Harrington HA, Restrepo JG, Taylor D. Dynamics on networks with higher-order interactions. CHAOS (WOODBURY, N.Y.) 2023; 33:040401. [PMID: 37097941 DOI: 10.1063/5.0151265] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Accepted: 03/22/2023] [Indexed: 06/19/2023]
Affiliation(s)
- Z Gao
- School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
| | - D Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - H A Harrington
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - J G Restrepo
- Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - D Taylor
- Department of Mathematics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
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13
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Nag Chowdhury S, Rakshit S, Hens C, Ghosh D. Interlayer antisynchronization in degree-biased duplex networks. Phys Rev E 2023; 107:034313. [PMID: 37073037 DOI: 10.1103/physreve.107.034313] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 03/09/2023] [Indexed: 04/20/2023]
Abstract
With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, California 95616, USA
- Technology Innovation Hub (TIH), IDEAS (Institute of Data Engineering Analytics and Science Foundation), Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Sarbendu Rakshit
- Department of Mechanical Engineering, University of California, Riverside, California 92521, USA
| | - Chittaranjan Hens
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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