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Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix

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  • Liu, Xiwei
  • Chen, Tianping

Abstract

In this paper, the global synchronization for an array of nonlinearly coupled identical chaotic systems is investigated. A distinctive feature of this work is to address synchronization issues for nonlinearly coupled complex networks with an asymmetrical coupling matrix. By projecting the nonlinear coupling function onto a linear one and assuming the difference between them as a disturbing function, we give some criteria for the global synchronization in virtual of the left eigenvector corresponding to the zero eigenvalue of the coupling matrix. Numerical examples are also provided to demonstrate the effectiveness of the theory.

Suggested Citation

  • Liu, Xiwei & Chen, Tianping, 2008. "Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4429-4439.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:16:p:4429-4439
    DOI: 10.1016/j.physa.2008.03.005
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    References listed on IDEAS

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    1. Liu, Xiwei & Chen, Tianping, 2007. "Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 82-92.
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    Cited by:

    1. Shi, Lin & Yang, Huilan & Wang, Xin & Zhong, Shouming & Wang, Wenqin, 2018. "Synchronization of complex networks with asymmetric coupling via decomposing matrix method," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 180-185.
    2. Bandyopadhyay, Abhirup & Kar, Samarjit, 2018. "Impact of network structure on synchronization of Hindmarsh–Rose neurons coupled in structured network," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 194-212.
    3. Zhou, Jiamu & Dong, Hailing & Feng, Jianwen, 2017. "Event-triggered communication for synchronization of Markovian jump delayed complex networks with partially unknown transition rates," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 617-629.
    4. Tseng, Jui-Pin, 2016. "A novel approach to synchronization of nonlinearly coupled network systems with delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 266-280.
    5. Cheng, Lin & Yang, Yongqing & Li, Li & Sui, Xin, 2018. "Finite-time hybrid projective synchronization of the drive-response complex networks with distributed-delay via adaptive intermittent control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 273-286.
    6. Shi, Tian & Qin, Yi & Yang, Qi & Ma, Zhongjun & Li, Kezan, 2023. "Synchronization of directed uniform hypergraphs via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    7. Xuan, Deli & Tang, Ze & Feng, Jianwen & Park, Ju H., 2021. "Cluster synchronization of nonlinearly coupled Lur’e networks: Delayed impulsive adaptive control protocols," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Jie Liu & Jian-Ping Sun, 2024. "Clustering Component Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control," Mathematics, MDPI, vol. 12(7), pages 1-17, March.
    9. Cheng, Ranran & Peng, Mingshu & Yu, Weibin, 2014. "Pinning synchronization of delayed complex dynamical networks with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 426-431.
    10. Chen, Xi & Luo, Maokang & Zhong, Yangfan & Zhang, Lu, 2022. "Collective dynamic behaviors of a general adjacent coupled chain in both unconfined and confined spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    11. Hu, Aihua & Cao, Jinde & Hu, Manfeng & Guo, Liuxiao, 2014. "Cluster synchronization in directed networks of non-identical systems with noises via random pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 537-548.
    12. Wang, Kun-Peng & Ding, Dong & Tang, Ze & Feng, Jianwen, 2022. "Leader-Following consensus of nonlinear multi-agent systems with hybrid delays: Distributed impulsive pinning strategy," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    13. Du, Hongyue, 2011. "Function projective synchronization in drive–response dynamical networks with non-identical nodes," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 510-514.
    14. Ding, Dong & Tang, Ze & Wang, Yan & Ji, Zhicheng, 2020. "Synchronization of nonlinearly coupled complex networks: Distributed impulsive method," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    15. Zhang, Hai & Ye, Miaolin & Ye, Renyu & Cao, Jinde, 2018. "Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 155-165.

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