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The stability of stochastic coupled systems with time delays and time-varying coupling structure

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  • Liu, Yan
  • Guo, Ying
  • Li, Wenxue

Abstract

This paper is concerned with the pth moment exponential stability of stochastic coupled systems with time delays and time-varying coupling structure (SCTVCS). The coupling structure is time-varying first. Second, the method of graph theory has been generalized from a system established on a digraph with constant coupling structure to a digraph with time-varying coupling structure successfully. Combining graph theory with Lyapunov method, a systematic method is given to construct a Lyapunov function for SCTVCS. Several pth moment exponential stability criteria are presented, including a Lyapunov-type theorem, and some sufficient criteria in the form of coefficients. Furthermore, the theoretical conclusions are applied to the stochastic coupled oscillators with time-varying coupling structure, and two stability criteria are obtained. Finally, we give two numerical examples to illustrate the effectiveness of our results.

Suggested Citation

  • Liu, Yan & Guo, Ying & Li, Wenxue, 2016. "The stability of stochastic coupled systems with time delays and time-varying coupling structure," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 507-520.
    • Handle: RePEc:eee:apmaco:v:290:y:2016:i:c:p:507-520
    DOI: 10.1016/j.amc.2016.06.029
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    References listed on IDEAS

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    1. Chen, Hao & Zhong, Shouming & Shao, Jinliang, 2015. "Exponential stability criterion for interval neural networks with discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 121-130.
    2. Gao, Shang & Wu, Boying, 2015. "On input-to-state stability for stochastic coupled control systems on networks," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 90-101.
    3. Zhang, Xinhong & Li, Wenxue & Wang, Ke, 2015. "The existence and global exponential stability of periodic solution for a neutral coupled system on networks with delays," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 208-217.
    4. Chen, Hao & Sun, Jitao, 2012. "Stability analysis for coupled systems with time delay on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 528-534.
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    Cited by:

    1. Zhang, Chunmei & Chen, Tianrui, 2018. "Exponential stability of stochastic complex networks with multi-weights based on graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 602-611.

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