1
|
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.
Collapse
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
| |
Collapse
|
2
|
Rathore V, Suman A, Jalan S. Synchronization onset for contrarians with higher-order interactions in multilayer systems. CHAOS (WOODBURY, N.Y.) 2023; 33:091105. [PMID: 37729103 DOI: 10.1063/5.0166627] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 08/28/2023] [Indexed: 09/22/2023]
Abstract
We investigate the impact of contrarians (via negative coupling) in multilayer networks of phase oscillators having higher-order interactions. We report that the multilayer framework facilitates synchronization onset in the negative pairwise coupling regime. The multilayering strength governs the onset of synchronization and the nature of the phase transition, whereas the higher-order interactions dictate the backward critical coupling. Specifically, the system does not synchronize below a critical value of the multilayering strength. The analytical calculations using the mean-field Ott-Antonsen approach agree with the simulations. The results presented here may be useful for understanding emergent behaviors in real-world complex systems with contrarians and higher-order interactions, such as the brain and social system.
Collapse
Affiliation(s)
- Vasundhara Rathore
- Department of Biosciences and Biomedical Engineering, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India
| | - Ayushi Suman
- Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India
| | - Sarika Jalan
- Department of Biosciences and Biomedical Engineering, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India
- Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India
| |
Collapse
|
3
|
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.
Collapse
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
| |
Collapse
|
4
|
Rathore V, Kachhvah AD, Jalan S. Catalytic feed-forward explosive synchronization in multilayer networks. CHAOS (WOODBURY, N.Y.) 2021; 31:123130. [PMID: 34972326 DOI: 10.1063/5.0060803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2021] [Accepted: 12/01/2021] [Indexed: 06/14/2023]
Abstract
Inhibitory couplings are crucial for the normal functioning of many real-world complex systems. Inhibition in one layer has been shown to induce explosive synchronization in another excitatory (or positive) layer of duplex networks. By extending this framework to multiplex networks, this article shows that inhibition in a single layer can act as a catalyst, leading to explosive synchronization transitions in the rest of the layers feed-forwarded through intermediate layer(s). Considering a multiplex network of coupled Kuramoto oscillators, we demonstrate that the characteristics of the transition emergent in a layer can be entirely controlled by the intra-layer coupling of other layers and the multiplexing strengths. The results presented here are essential to fathom the synchronization behavior of coupled dynamical units in multi-layer systems possessing inhibitory coupling in one of its layers, representing the importance of multiplexing.
Collapse
Affiliation(s)
- Vasundhara Rathore
- Department of Biosciences and Biomedical Engineering, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India
| | - Ajay Deep Kachhvah
- Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India
| | - Sarika Jalan
- Department of Biosciences and Biomedical Engineering, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India
| |
Collapse
|
5
|
Vandermeer J, Hajian-Forooshani Z, Medina N, Perfecto I. New forms of structure in ecosystems revealed with the Kuramoto model. ROYAL SOCIETY OPEN SCIENCE 2021; 8:210122. [PMID: 33959373 PMCID: PMC8074911 DOI: 10.1098/rsos.210122] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 02/10/2021] [Indexed: 06/12/2023]
Abstract
Ecological systems, as is often noted, are complex. Equally notable is the generalization that complex systems tend to be oscillatory, whether Huygens' simple patterns of pendulum entrainment or the twisted chaotic orbits of Lorenz' convection rolls. The analytics of oscillators may thus provide insight into the structure of ecological systems. One of the most popular analytical tools for such study is the Kuramoto model of coupled oscillators. We apply this model as a stylized vision of the dynamics of a well-studied system of pests and their enemies, to ask whether its actual natural history is reflected in the dynamics of the qualitatively instantiated Kuramoto model. Emerging from the model is a series of synchrony groups generally corresponding to subnetworks of the natural system, with an overlying chimeric structure, depending on the strength of the inter-oscillator coupling. We conclude that the Kuramoto model presents a novel window through which interesting questions about the structure of ecological systems may emerge.
Collapse
Affiliation(s)
- John Vandermeer
- Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI 481090, USA
- Program in the Environment, University of Michigan, Ann Arbor, MI 481090, USA
| | | | - Nicholas Medina
- Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI 481090, USA
| | - Ivette Perfecto
- Program in the Environment, University of Michigan, Ann Arbor, MI 481090, USA
- School for Environment and Sustainability, University of Michigan, Ann Arbor, MI 481090, USA
| |
Collapse
|
6
|
Fan H, Kong LW, Wang X, Hastings A, Lai YC. Synchronization within synchronization: transients and intermittency in ecological networks. Natl Sci Rev 2020; 8:nwaa269. [PMID: 34858600 PMCID: PMC8566182 DOI: 10.1093/nsr/nwaa269] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2020] [Revised: 09/28/2020] [Accepted: 09/28/2020] [Indexed: 11/13/2022] Open
Abstract
Transients are fundamental to ecological systems with significant implications to management, conservation and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator–prey type. In the parameter regime where there is phase synchronization among all the patches, complete synchronization (i.e. synchronization in both phase and amplitude) can arise in certain pairs of patches as determined by the network symmetry—henceforth the phenomenon of ‘synchronization within synchronization.’ Distinct patterns of complete synchronization coexist but, due to intrinsic instability or noise, each pattern is a transient and there is random, intermittent switching among the patterns in the course of time evolution. The probability distribution of the transient time is found to follow an algebraic scaling law with a divergent average transient lifetime. Based on symmetry considerations, we develop a stability analysis to understand these phenomena. The general principle of symmetry can also be exploited to explain previously discovered, counterintuitive synchronization behaviors in ecological networks.
Collapse
Affiliation(s)
- Huawei Fan
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Ling-Wei Kong
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA
| | - Xingang Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Alan Hastings
- Department of Environmental Science and Policy, University of California, Davis, CA 95616, USA
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA
| |
Collapse
|
7
|
Bera BK. Additional repulsion reduces the dynamical resilience in the damaged networks. CHAOS (WOODBURY, N.Y.) 2020; 30:023132. [PMID: 32113231 DOI: 10.1063/1.5130543] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2019] [Accepted: 02/05/2020] [Indexed: 06/10/2023]
Abstract
In this paper, we investigate the dynamical robustness of diffusively coupled oscillatory networks under the influence of an additional repulsive link. Such a dynamical resilience property is realized through the aging process of the damaged network of active and inactive oscillators. The aging process is one type of phase transition, mainly appearing at a critical threshold of a fraction of the inactive oscillator node where the mean oscillation amplitude of the entire network suddenly vanishes. These critical fractions of the failure nodes in the network are broadly used as a measure of network resilience. Here, we analytically derived the critical fraction of the aging process in the dynamical network. We find that the addition of the repulsive link enhances the critical threshold of the aging transition of diffusively coupled oscillators, which indicated that the dynamical robustness of the coupled network decreases with the presence of the repulsive interaction. Furthermore, we investigate the dynamical robustness of the network against the number of deteriorating repulsive links. We observed that a certain percentage of the repulsive link is enabled to produce the aging process in the entire network. Finally, the effect of symmetry-breaking coupling and the targeted inactivation process on the dynamical robustness property of damaged networks were investigated. The analytically obtained results are verified numerically in the network of coupled Stuart-Landau oscillators. These findings may help us to better understand the role of the coupling mechanism on the phase transition in the damaged network.
Collapse
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
| |
Collapse
|
8
|
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.
Collapse
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
| |
Collapse
|
9
|
Uwate Y, Nishio Y. Competitive networks using chaotic circuits with hierarchical structure. CHAOS (WOODBURY, N.Y.) 2019; 29:083115. [PMID: 31472511 DOI: 10.1063/1.5093331] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2019] [Accepted: 07/16/2019] [Indexed: 06/10/2023]
Abstract
Coupled oscillatory systems are good models that are able to describe a variety of higher dimensional nonlinear phenomena. Coupled chaotic circuits produce many kinds of interesting synchronization phenomena. In recent years, research studies on complex networks related to the synchronization of coupled oscillators have attracted much attention. In the real world, there are a variety of different network structures. We focus on the competitive interaction network that includes conflict between two networks. Here, we propose a new paradigm for this competitive interaction network using coupled chaotic circuits.
Collapse
Affiliation(s)
- Y Uwate
- Department of Electrical and Electronics Engineering, Tokushima University, 2-1 Minami Josanjima, Tokushima 770-8506, Japan
| | - Y Nishio
- Department of Electrical and Electronics Engineering, Tokushima University, 2-1 Minami Josanjima, Tokushima 770-8506, Japan
| |
Collapse
|
10
|
Jalan S, Rathore V, Kachhvah AD, Yadav A. Inhibition-induced explosive synchronization in multiplex networks. Phys Rev E 2019; 99:062305. [PMID: 31330578 DOI: 10.1103/physreve.99.062305] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2018] [Indexed: 06/10/2023]
Abstract
To date, explosive synchronization (ES) in a network is shown to be originated from considering either degree-frequency correlation, frequency-coupling strength correlation, inertia, or adaptively controlled phase oscillators. Here we show that ES is a generic phenomenon and can occur in any network by multiplexing it with an appropriate layer without even considering any prerequisite for the emergence of ES. We devise a technique which leads to the occurrence of ES with hysteresis loop in a network upon its multiplexing with a negatively coupled (or inhibitory) layer. The impact of various structural properties of positively coupled (or excitatory) and inhibitory layers along with the strength of multiplexing in gaining control over the induced ES transition is discussed. Analytical prediction for the spread of phase distribution of each layer is provided, which is in good agreement with the numerical assessment. This investigation is a step forward in highlighting the importance of multiplex framework not only in bringing phenomena which are not possible in an isolated network but also in providing more structural control over the induced phenomena.
Collapse
Affiliation(s)
- Sarika Jalan
- Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453552, India
- Discipline of Biosciences and Biomedical Engineering, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453552, India
- Laboratory of Systems Medicine of Healthy Aging and Department of Applied Mathematics, Lobachevsky University, Nizhny Novgorod, Russia
| | - Vasundhara Rathore
- Discipline of Biosciences and Biomedical Engineering, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453552, India
| | - Ajay Deep Kachhvah
- Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453552, India
| | - Alok Yadav
- Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453552, India
| |
Collapse
|