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Global exponential convergence of generalized chaotic systems with multiple time-varying and finite distributed delays

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  • Jian, Jigui
  • Wan, Peng

Abstract

Under some simple conditions, the convergence of a generalized chaotic system about its all variables is derived by only considering the convergence of its partial variables. Furthermore, based on some inequality techniques and employing the Lyapunov method, some novel sufficient criteria are derived to ensure the state variables of the discussed mixed delay system to converge, globally exponentially to a ball in the state space with a pre-specified convergence rate. Meanwhile, the ultimate bounds of the generalized chaotic system about its all variables are induced by the ultimate bounds of the system about its partial variables. Moreover, the maximum convergence rates about partial variables are also given. The methods are simple and valid for the convergence analysis of systems with time-varying and finite distributed delays. Here, the existence and uniqueness of the equilibrium point needs not to be considered. These simple conditions here are easy to be verified in engineering applications. Finally, some illustrated examples are given to show the effectiveness and usefulness of the results.

Suggested Citation

  • Jian, Jigui & Wan, Peng, 2015. "Global exponential convergence of generalized chaotic systems with multiple time-varying and finite distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 152-165.
    • Handle: RePEc:eee:phsmap:v:431:y:2015:i:c:p:152-165
    DOI: 10.1016/j.physa.2015.03.001
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    References listed on IDEAS

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    1. Xiong, Wenjun & Ma, Deyi & Liang, Jinling, 2009. "Robust convergence of Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1176-1184.
    2. Xiong, Wenjun & Xie, Wei & Cao, Jinde, 2006. "Adaptive exponential synchronization of delayed chaotic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 832-842.
    3. Wang, Kai & Teng, Zhidong & Jiang, Haijun, 2008. "Adaptive synchronization of neural networks with time-varying delay and distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 631-642.
    4. Long, Shujun & Wang, Xiaohu & Li, Dingshi, 2012. "Attracting and invariant sets of non-autonomous reaction-diffusion neural networks with time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(11), pages 2199-2214.
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    Cited by:

    1. Xu, Changjin & Li, Peiluan, 2017. "Global exponential convergence of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 139-144.
    2. Peng, Qiu & Jian, Jigui, 2021. "Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Jian, Jigui & Wu, Kai & Wang, Baoxian, 2020. "Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

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