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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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Leo Kingston S, Kumaran G, Ghosh A, Kumarasamy S, Kapitaniak T. Impact of time varying interaction: Formation and annihilation of extreme events in dynamical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:123134. [PMID: 38154041 DOI: 10.1063/5.0174366] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2023] [Accepted: 11/30/2023] [Indexed: 12/30/2023]
Abstract
This study investigates the emergence of extreme events in two different coupled systems: the FitzHugh-Nagumo neuron model and the forced Liénard system, both based on time-varying interactions. The time-varying coupling function between the systems determines the duration and frequency of their interaction. Extreme events in the coupled system arise as a result of the influence of time-varying interactions within various parameter regions. We specifically focus on elucidating how the transition point between extreme events and regular events shifts in response to the duration of interaction time between the systems. By selecting the appropriate interaction time, we can effectively mitigate extreme events, which is highly advantageous for controlling undesired fluctuations in engineering applications. Furthermore, we extend our investigation to networks of oscillators, where the interactions among network elements are also time dependent. The proposed approach for coupled systems holds wide applicability to oscillator networks.
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Affiliation(s)
- S Leo Kingston
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Gayathri Kumaran
- Department of Electronics and Communication Engineering, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Anupam Ghosh
- Department of Complex Systems, Institute of Computer Science, Czech Academy of Sciences, Prague 18207, Czech Republic
| | - Suresh Kumarasamy
- Centre for Computational Modeling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
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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: 2] [Impact Index Per Article: 2.0] [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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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: 0] [Impact Index Per Article: 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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Roy S, Nag Chowdhury S, Mali PC, Perc M, Ghosh D. Eco-evolutionary dynamics of multigames with mutations. PLoS One 2022; 17:e0272719. [PMID: 35944035 PMCID: PMC9362954 DOI: 10.1371/journal.pone.0272719] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 07/25/2022] [Indexed: 11/30/2022] Open
Abstract
Most environments favor defection over cooperation due to natural selection. Nonetheless, the emergence of cooperation is omnipresent in many biological, social, and economic systems, quite contrary to the well-celebrated Darwinian theory of evolution. Much research has been devoted to better understanding how and why cooperation persists among self-interested individuals despite their competition for limited resources. Here we go beyond a single social dilemma since individuals usually encounter various social challenges. In particular, we propose and study a mathematical model incorporating both the prisoner’s dilemma and the snowdrift game. We further extend this model by considering ecological signatures like mutation and selfless one-sided contribution of altruist free space. The nonlinear evolutionary dynamics that results from these upgrades offer a broader range of equilibrium outcomes, and it also often favors cooperation over defection. With the help of analytical and numerical calculations, our theoretical model sheds light on the mechanisms that maintain biodiversity, and it helps to explain the evolution of social order in human societies.
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Affiliation(s)
- Sourav Roy
- Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India
| | - Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, India
| | | | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Alma Mater Europaea, Maribor, Slovenia
- Complexity Science Hub Vienna, Vienna, Austria
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, India
- * E-mail:
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Dixit S, Aravind M, Parmananda P. Regulating dynamics through intermittent interactions. Phys Rev E 2022; 106:014203. [PMID: 35974523 DOI: 10.1103/physreve.106.014203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 05/23/2022] [Indexed: 06/15/2023]
Abstract
In this article we experimentally demonstrate an efficient scheme to regulate the behavior of coupled nonlinear oscillators through dynamic control of their interaction. It is observed that introducing intermittency in the interaction term as a function of time or the system state predictably alters the dynamics of the constituent oscillators. Choosing the nature of the interaction, attractive or repulsive, allows for either suppression of oscillations or stimulation of activity. Two parameters Δ and τ, that reign the extent of interaction among subsystems, are introduced. They serve as a harness to access the entire range of possible behaviors from fixed points to chaos. For fixed values of system parameters and coupling strength, changing Δ and τ offers fine control over the dynamics of coupled subsystems. We show this experimentally using coupled Chua's circuits and elucidate their behavior for a range of coupling parameters through detailed numerical simulations.
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Affiliation(s)
- Shiva Dixit
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Manaoj Aravind
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
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Chowdhury SN, Rakshit S, Buldú JM, Ghosh D, Hens C. Antiphase synchronization in multiplex networks with attractive and repulsive interactions. Phys Rev E 2021; 103:032310. [PMID: 33862752 DOI: 10.1103/physreve.103.032310] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 02/16/2021] [Indexed: 06/12/2023]
Abstract
A series of recent publications, within the framework of network science, have focused on the coexistence of mixed attractive and repulsive (excitatory and inhibitory) interactions among the units within the same system, motivated by the analogies with spin glasses as well as to neural networks, or ecological systems. However, most of these investigations have been restricted to single layer networks, requiring further analysis of the complex dynamics and particular equilibrium states that emerge in multilayer configurations. This article investigates the synchronization properties of dynamical systems connected through multiplex architectures in the presence of attractive intralayer and repulsive interlayer connections. This setting enables the emergence of antisynchronization, i.e., intralayer synchronization coexisting with antiphase dynamics between coupled systems of different layers. We demonstrate the existence of a transition from interlayer antisynchronization to antiphase synchrony in any connected bipartite multiplex architecture when the repulsive coupling is introduced through any spanning tree of a single layer. We identify, analytically, the required graph topologies for interlayer antisynchronization and its interplay with intralayer and antiphase synchronization. Next, we analytically derive the invariance of intralayer synchronization manifold and calculate the attractor size of each oscillator exhibiting interlayer antisynchronization together with intralayer synchronization. The necessary conditions for the existence of interlayer antisynchronization along with intralayer synchronization are given and numerically validated by considering Stuart-Landau oscillators. Finally, we also analytically derive the local stability condition of the interlayer antisynchronization state using the master stability function approach.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | - Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | - Javier M Buldú
- Laboratory of Biological Networks, Center for Biomedical Technology-UPM, Madrid 28223, Spain
- Complex Systems Group and GISC, Universidad Rey Juan Carlos, Móstoles 28933, Spain
- Unmanned Systems Research Institute, Northwestern Polytechnical University, Xi'an 710072, China
| | - 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
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Dixit S, Nag Chowdhury S, Prasad A, Ghosh D, Shrimali MD. Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions. CHAOS (WOODBURY, N.Y.) 2021; 31:011105. [PMID: 33754786 DOI: 10.1063/5.0039879] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 12/29/2020] [Indexed: 06/12/2023]
Abstract
The role of a new form of dynamic interaction is explored in a network of generic identical oscillators. The proposed design of dynamic coupling facilitates the onset of a plethora of asymptotic states including synchronous states, amplitude death states, oscillation death states, a mixed state (complete synchronized cluster and small amplitude desynchronized domain), and bistable states (coexistence of two attractors). The dynamical transitions from the oscillatory to the death state are characterized using an average temporal interaction approximation, which agrees with the numerical results in temporal interaction. A first-order phase transition behavior may change into a second-order transition in spatial dynamic interaction solely depending on the choice of initial conditions in the bistable regime. However, this possible abrupt first-order like transition is completely non-existent in the case of temporal dynamic interaction. Besides the study on periodic Stuart-Landau systems, we present results for the paradigmatic chaotic model of Rössler oscillators and the MacArthur ecological model.
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Affiliation(s)
- Shiva Dixit
- Department of Physics, Central University of Rajasthan, NH-8,Bandar Sindri, Ajmer 305 817, India
| | - Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Awadhesh Prasad
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Manish Dev Shrimali
- Department of Physics, Central University of Rajasthan, NH-8,Bandar Sindri, Ajmer 305 817, India
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Dixit S, Shrimali MD. Static and dynamic attractive-repulsive interactions in two coupled nonlinear oscillators. CHAOS (WOODBURY, N.Y.) 2020; 30:033114. [PMID: 32237763 DOI: 10.1063/1.5127249] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Accepted: 02/16/2020] [Indexed: 06/11/2023]
Abstract
Many systems exhibit both attractive and repulsive types of interactions, which may be dynamic or static. A detailed understanding of the dynamical properties of a system under the influence of dynamically switching attractive or repulsive interactions is of practical significance. However, it can also be effectively modeled with two coexisting competing interactions. In this work, we investigate the effect of time-varying attractive-repulsive interactions as well as the hybrid model of coexisting attractive-repulsive interactions in two coupled nonlinear oscillators. The dynamics of two coupled nonlinear oscillators, specifically limit cycles as well as chaotic oscillators, are studied in detail for various dynamical transitions for both cases. Here, we show that dynamic or static attractive-repulsive interactions can induce an important transition from the oscillatory to steady state in identical nonlinear oscillators due to competitive effects. The analytical condition for the stable steady state in dynamic interactions at the low switching time period and static coexisting interactions are calculated using linear stability analysis, which is found to be in good agreement with the numerical results. In the case of a high switching time period, oscillations are revived for higher interaction strength.
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Affiliation(s)
- Shiva Dixit
- Department of Physics, Central University of Rajasthan, NH-8, Bandar Sindri, Ajmer 305 817, India
| | - Manish Dev Shrimali
- Department of Physics, Central University of Rajasthan, NH-8, Bandar Sindri, Ajmer 305 817, India
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Rakshit S, Bera BK, Kurths J, Ghosh D. Enhancing synchrony in multiplex network due to rewiring frequency. Proc Math Phys Eng Sci 2019. [DOI: 10.1098/rspa.2019.0460] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Most of the previous studies on synchrony in multiplex networks have been investigated using different types of intralayer network architectures which are either static or temporal. Effect of a temporal layer on intralayer synchrony in a multilayered network still remains elusive. In this paper, we discuss intralayer synchrony in a multiplex network consisting of static and temporal layers and how a temporal layer influences other static layers to enhance synchrony simultaneously. We analytically derive local stability conditions for intralayer synchrony based on the master stability function approach. The analytically derived results are illustrated by numerical simulations on up to five-layers multiplex networks with the paradigmatic Lorenz system as the node dynamics in each individual layer.
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Affiliation(s)
- Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Bidesh K. Bera
- Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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