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Ghosh R, Verma UK, Jalan S, Shrimali MD. Chimeric states induced by higher-order interactions in coupled prey-predator systems. CHAOS (WOODBURY, N.Y.) 2024; 34:061101. [PMID: 38829788 DOI: 10.1063/5.0213288] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2024] [Accepted: 05/12/2024] [Indexed: 06/05/2024]
Abstract
Higher-order interactions have been instrumental in characterizing the intricate complex dynamics in a diverse range of large-scale complex systems. Our study investigates the effect of attractive and repulsive higher-order interactions in globally and non-locally coupled prey-predator Rosenzweig-MacArthur systems. Such interactions lead to the emergence of complex spatiotemporal chimeric states, which are otherwise unobserved in the model system with only pairwise interactions. Our model system exhibits a second-order transition from a chimera-like state (mixture of oscillating and steady state nodes) to a chimera-death state through a supercritical Hopf bifurcation. The origin of these states is discussed in detail along with the effect of the higher-order non-local topology which leads to the rise of a distinct and dynamical state termed as "amplitude-mediated chimera-like states." Our study observes that the introduction of higher-order attractive and repulsive interactions exhibit incoherence and promote persistence in consumer-resource population dynamics as opposed to susceptibility shown by synchronized dynamics with only pairwise interactions, and these results may be of interest to conservationists and theoretical ecologists studying the effect of competing interactions in ecological networks.
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Affiliation(s)
- Richita Ghosh
- Department of Physics, Central University of Rajasthan, Rajasthan, Ajmer 305 817, India
| | - Umesh Kumar Verma
- Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453 552, India
| | - Sarika Jalan
- Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453 552, India
| | - Manish Dev Shrimali
- Department of Physics, Central University of Rajasthan, Rajasthan, Ajmer 305 817, India
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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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3
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Rybalova E, Muni S, Strelkova G. Transition from chimera/solitary states to traveling waves. CHAOS (WOODBURY, N.Y.) 2023; 33:033104. [PMID: 37003811 DOI: 10.1063/5.0138207] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Accepted: 02/08/2023] [Indexed: 06/19/2023]
Abstract
We study numerically the spatiotemporal dynamics in a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. It is shown that the discretized oscillator exhibits richer behavior, combining the peculiarities of both the original system and its own dynamics. Moreover, a large variety of spatiotemporal structures is observed in the network of discrete van der Pol oscillators when the discretization parameter and the coupling strength are varied. Regimes, such as the coexistence of a multichimera state/a traveling wave and a solitary state are revealed for the first time and are studied in detail. It is established that the majority of the observed chimera/solitary states, including the newly found ones, are transient toward a purely traveling wave mode. The peculiarities of the transition process and the lifetime (transient duration) of the chimera structures and the solitary state are analyzed depending on the system parameters, the observation time, initial conditions, and the influence of external noise.
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Affiliation(s)
- E Rybalova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - S Muni
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Campus Road, Mohanpur, West Bengal 741246, India
| | - G Strelkova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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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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5
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Schülen L, Gerdes A, Wolfrum M, Zakharova A. Solitary routes to chimera states. Phys Rev E 2022; 106:L042203. [PMID: 36397505 DOI: 10.1103/physreve.106.l042203] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 09/26/2022] [Indexed: 06/16/2023]
Abstract
We show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit we demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. We demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators.
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Affiliation(s)
- Leonhard Schülen
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Alexander Gerdes
- Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany
| | - Matthias Wolfrum
- Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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Bera BK, Kundu S, Muruganandam P, Ghosh D, Lakshmanan M. Spiral wave chimera-like transient dynamics in three-dimensional grid of diffusive ecological systems. CHAOS (WOODBURY, N.Y.) 2021; 31:083125. [PMID: 34470253 DOI: 10.1063/5.0062566] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Accepted: 08/04/2021] [Indexed: 06/13/2023]
Abstract
In the present article, we demonstrate the emergence and existence of the spiral wave chimera-like transient pattern in coupled ecological systems, composed of prey-predator patches, where the patches are connected in a three-dimensional medium through local diffusion. We explore the transition scenarios among several collective dynamical behaviors together with transient spiral wave chimera-like states and investigate the long time behavior of these states. The transition from the transient spiral chimera-like pattern to the long time synchronized or desynchronized pattern appears through the deformation of the incoherent region of the spiral core. We discuss the transient dynamics under the influence of the species diffusion at different time instants. By calculating the instantaneous strength of incoherence of the populations, we estimate the duration of the transient dynamics characterized by the persistence of the chimera-like spatial coexistence of coherent and incoherent patterns over the spatial domain. We generalize our observations on the transient dynamics in a three-dimensional grid of diffusive ecological systems by considering two different prey-predator systems.
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Affiliation(s)
- Bidesh K Bera
- Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
| | - Srilena Kundu
- Physics and Applied Mathematics Unit, 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
| | - M Lakshmanan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620024, 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: 18] [Impact Index Per Article: 6.0] [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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Bahramian A, Parastesh F, Pham VT, Kapitaniak T, Jafari S, Perc M. Collective behavior in a two-layer neuronal network with time-varying chemical connections that are controlled by a Petri net. CHAOS (WOODBURY, N.Y.) 2021; 31:033138. [PMID: 33810759 DOI: 10.1063/5.0045840] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 03/02/2021] [Indexed: 06/12/2023]
Abstract
In this paper, we propose and study a two-layer network composed of a Petri net in the first layer and a ring of coupled Hindmarsh-Rose neurons in the second layer. Petri nets are appropriate platforms not only for describing sequential processes but also for modeling information circulation in complex systems. Networks of neurons, on the other hand, are commonly used to study synchronization and other forms of collective behavior. Thus, merging both frameworks into a single model promises fascinating new insights into neuronal collective behavior that is subject to changes in network connectivity. In our case, the Petri net in the first layer manages the existence of excitatory and inhibitory links among the neurons in the second layer, thereby making the chemical connections time-varying. We focus on the emergence of different types of collective behavior in the model, such as synchronization, chimeras, and solitary states, by considering different inhibitory and excitatory tokens in the Petri net. We find that the existence of only inhibitory or excitatory tokens disturbs the synchronization of electrically coupled neurons and leads toward chimera and solitary states.
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Affiliation(s)
- Alireza Bahramian
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave., Valiasr Square, Tehran 159163-4311, Iran
| | - Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave., Valiasr Square, Tehran 159163-4311, Iran
| | - Viet-Thanh Pham
- Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Sajad Jafari
- Center for Computational Biology, Chennai Institute of Technology, Chennai, Tamil Nadu 600069, India
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
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Dudkowski D, Czołczyński K, Kapitaniak T. Multi-headed loop chimera states in coupled oscillators. CHAOS (WOODBURY, N.Y.) 2021; 31:013135. [PMID: 33754776 DOI: 10.1063/5.0033519] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Accepted: 01/05/2021] [Indexed: 06/12/2023]
Abstract
In this paper, we introduce a novel type of chimera state, characterized by the geometrical distortion of the coherent ring topology of coupled oscillators. The multi-headed loop chimeras are examined for a simple network of locally coupled pendulum clocks, suspended on the vertical platform. We determine the regions of the occurrence of the observed patterns, their structure, and possible co-existence. The representative examples of behaviors are shown, exhibiting the variety of configurations that can be observed. The statistical analysis of the solutions indicates the geometrical regions of the system with the highest probability of the chimeras' occurrence. We investigate the mechanism of the creation of the observed states, showing that the manipulation of the initial positions of chosen pendula may induce the desired patterns. Apart from the study of the isolated network, we also discuss the scenario of the movable platform, showing a possible influence of the global coupling structure on the stability of the observed states. The stability of loop chimeras is examined for varying both the amplitude and the frequency of the oscillations of the platform. We indicate the excitation parameters for which the solutions can survive as well as be destroyed. The bifurcation analysis included in the paper allows us to discuss the transitions between possible behaviors. The appearance of multi-headed loop chimeras is generalized into large networks of oscillators, showing the universal character of the observed patterns. One should expect to observe similar results also in other types of coupled oscillators, especially the mechanical ones.
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Affiliation(s)
- Dawid Dudkowski
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Krzysztof Czołczyński
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
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Chowdhury SN, Ghosh D, Hens C. Effect of repulsive links on frustration in attractively coupled networks. Phys Rev E 2020; 101:022310. [PMID: 32168719 DOI: 10.1103/physreve.101.022310] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2019] [Accepted: 01/31/2020] [Indexed: 06/10/2023]
Abstract
We investigate the impact of attractive-repulsive interaction in networks of limit cycle oscillators. Mainly we focus on the design principle for generating an antiphase state between adjacent nodes in a complex network. We establish that a partial negative control throughout the branches of a spanning tree inside the positively coupled limit cycle oscillators works efficiently well in comparison with randomly chosen negative links to establish zero frustration (antiphase synchronization) in bipartite graphs. Based on the emergence of zero frustration, we develop a universal 0-π rule to understand the antiphase synchronization in a bipartite graph. Further, this rule is used to construct a nonbipartite graph for a given nonzero frustrated value. We finally show the generality of 0-π rule by implementing it in arbitrary undirected nonbipartite graphs of attractive-repulsively coupled limit cycle oscillators and successfully calculate the nonzero frustration value, which matches with numerical data. The validation of the rule is checked through the bifurcation analysis of small networks. Our work may unveil the underlying mechanism of several synchronization phenomena that exist in a network of oscillators having a mixed type of coupling.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, 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
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Teichmann E, Rosenblum M. Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions. CHAOS (WOODBURY, N.Y.) 2019; 29:093124. [PMID: 31575139 DOI: 10.1063/1.5118843] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Accepted: 09/04/2019] [Indexed: 06/10/2023]
Abstract
We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group are identical, but natural frequencies of the groups differ. In addition to a synchronous two-cluster state, the system exhibits a solitary state, when a single oscillator leaves the cluster of repulsive elements, as well as partially synchronous quasiperiodic dynamics. We demonstrate how the transitions between these states occur when the repulsion starts to prevail over attraction.
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Affiliation(s)
- Erik Teichmann
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
| | - Michael Rosenblum
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
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