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Synchronization in an array of linearly stochastically coupled networks with time delays

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  • Cao, Jinde
  • Wang, Zidong
  • Sun, Yonghui

Abstract

In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.

Suggested Citation

  • Cao, Jinde & Wang, Zidong & Sun, Yonghui, 2007. "Synchronization in an array of linearly stochastically coupled networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 718-728.
    • Handle: RePEc:eee:phsmap:v:385:y:2007:i:2:p:718-728
    DOI: 10.1016/j.physa.2007.06.043
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    References listed on IDEAS

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    1. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
    2. Lü, Jinhu & Yu, Xinghuo & Chen, Guanrong, 2004. "Chaos synchronization of general complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 281-302.
    3. Wang, Weiwei & Cao, Jinde, 2006. "Synchronization in an array of linearly coupled networks with time-varying delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 197-211.
    4. Li, C.P. & Sun, W.G. & Kurths, J., 2006. "Synchronization of complex dynamical networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 24-34.
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    Cited by:

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    2. Qing Guo & Fangyi Wan, 2017. "Complete synchronization of the global coupled dynamical network induced by Poisson noises," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-11, December.
    3. Hu, Xiaohui & Xia, Jianwei & Wei, Yunliang & Meng, Bo & Shen, Hao, 2019. "Passivity-based state synchronization for semi-Markov jump coupled chaotic neural networks with randomly occurring time delays," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 32-41.
    4. Xie, Qian & Si, Gangquan & Zhang, Yanbin & Yuan, Yiwei & Yao, Rui, 2016. "Finite-time synchronization and identification of complex delayed networks with Markovian jumping parameters and stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 35-49.
    5. 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.
    6. Yang, Xinsong & Huang, Chuangxia & Zhu, Quanxin, 2011. "Synchronization of switched neural networks with mixed delays via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 817-826.
    7. Zhang, Chuan & Wang, Xingyuan & Luo, Chao & Li, Junqiu & Wang, Chunpeng, 2018. "Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 251-264.
    8. Cui, Xueke & Li, Hong-Li & Zhang, Long & Hu, Cheng & Bao, Haibo, 2023. "Complete synchronization for discrete-time fractional-order coupled neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    9. 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.
    10. Djeundam, S.R. Dtchetgnia & Filatrella, G. & Yamapi, R., 2018. "Desynchronization effects of a current-driven noisy Hindmarsh–Rose neural network," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 204-211.

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