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Emergence of synchronous behavior in a network with chaotic multistable systems

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  • Ruiz-Silva, A.
  • Gilardi-Velázquez, H.E.
  • Campos, Eric

Abstract

In this work, we address the synchronization problem of complex dynamical networks with bidirectional, linear, and diffusive coupling, whose nodes have dynamics given by a particular class of piecewise linear (PWL) systems. The class of PWL systems are multistable unstable dissipative systems and exhibit chaotic behavior. The topologies that we consider are regular coupled network. Firstly, we consider that the complex network has a uniform coupling strength, and through the Lyapunov approach, we show that nodes can achieve complete or partial synchronization, where the synchronization solution depends on the inner coupling matrix and the initial conditions of each node. Secondly, we consider a weighted network, where the synchronization solution depends on the external coupling matrix, and even obtain a synchronous behavior type master-slave. Our theoretical results agree with the numerical simulations for a set of nodes in different topology networks.

Suggested Citation

  • Ruiz-Silva, A. & Gilardi-Velázquez, H.E. & Campos, Eric, 2021. "Emergence of synchronous behavior in a network with chaotic multistable systems," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006172
    DOI: 10.1016/j.chaos.2021.111263
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    References listed on IDEAS

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    1. Chandrakala Meena & Pranay Deep Rungta & Sudeshna Sinha, 2020. "Resilience of networks of multi-stable chaotic systems to targetted attacks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(11), pages 1-9, November.
    2. Soriano-Sánchez, A.G. & Posadas-Castillo, C. & Platas-Garza, M.A. & Cruz-Hernández, C. & López-Gutiérrez, R.M., 2016. "Coupling strength computation for chaotic synchronization of complex networks with multi-scroll attractors," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 305-316.
    3. Ruiz-Silva, Adriana & Barajas-Ramírez, Juan Gonzalo, 2018. "Cluster synchronization in networks of structured communities," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 169-177.
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    Cited by:

    1. Bao, Han & Ding, Ruoyu & Chen, Bei & Xu, Quan & Bao, Bocheng, 2023. "Two-dimensional non-autonomous neuron model with parameter-controlled multi-scroll chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Serrano, Fernando E. & Ghosh, Dibakar, 2022. "Robust stabilization and synchronization in a network of chaotic systems with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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