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Cluster synchronization in networks of structured communities

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  • Ruiz-Silva, Adriana
  • Barajas-Ramírez, Juan Gonzalo

Abstract

We investigate the synchronization problem for a network of subnetwork with community structure. We consider a model with different levels of interconnection: At the first, strongly coupled adjacent nodes are modeled as a compact unit (CU) where connections are uniformed and undirected. A second level of connection occurs as CUs with similar dynamic behaviors from communities by weighted and undirected interactions. Finally a third level of connection, where directed and weighted connections between these communities form the entire network of subnetworks. Using the Lyapunov approach we show that cluster synchronization is possible for our network model where even though all nodes are interconnected each community achieves complete synchronization within, while the behavior between communities is not synchronized. Our main results are illustrated using numerical simulations of well-known benchmark systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:169-177
    DOI: 10.1016/j.chaos.2018.06.002
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    References listed on IDEAS

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    1. Liu, Meng & Shao, Yingying & Fu, Xinchu, 2009. "Complete synchronization on multi-layer center dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2584-2591.
    2. Fang Liu & Qiang Song & Jinde Cao & Jianquan Lu, 2014. "Pinning Synchronization of One-Sided Lipschitz Complex Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, April.
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    Cited by:

    1. Sun, Yanqin & Wu, Huaiyu & Chen, Zhihuan & Zheng, Xiujuan & Chen, Yang, 2021. "Outer synchronization of two different multi-links complex networks by chattering-free control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    2. 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).

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