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Input-to-state stability for stochastic multi-group models with multi-dispersal and time-varying delay

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  • Guo, Ying
  • Zhao, Wei
  • Ding, Xiaohua

Abstract

In this paper, the input-to-state stability (ISS) for a general class of stochastic multi-group models with multi-dispersal and time-varying delay is investigated. By means of graph theory and Lyapunov method as well as stochastic analysis techniques, sufficient criteria including a Lyapunov-type theorem and a coefficient-type theorem are obtained to guarantee that the proposed model is input-to-state stable. In addition, to show the applicability of our findings, the coefficient-type theorem is employed to study the ISS of stochastic coupled oscillators with time-varying delay and control input. Finally, a numerical example is offered to illustrate the effectiveness of the theoretical results.

Suggested Citation

  • Guo, Ying & Zhao, Wei & Ding, Xiaohua, 2019. "Input-to-state stability for stochastic multi-group models with multi-dispersal and time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 114-127.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:114-127
    DOI: 10.1016/j.amc.2018.07.058
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    References listed on IDEAS

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    1. 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.
    2. Yan, Zhiguo & Park, Ju H. & Zhang, Weihai, 2018. "A unified framework for asymptotic and transient behavior of linear stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 31-40.
    3. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    4. Xiaoming Fan & Zhigang Wang & Xuelian Xu, 2012. "Global Stability of Two-Group Epidemic Models with Distributed Delays and Random Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, March.
    5. Yan, Zhiguo & Song, Yunxia & Liu, Xiaoping, 2018. "Finite-time stability and stabilization for Itô-type stochastic Markovian jump systems with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 512-525.
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    Cited by:

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    3. Xin Liu & Lili Chen & Yanfeng Zhao, 2023. "Existence Theoremsfor Solutions of a Nonlinear Fractional-Order Coupled Delayed System via Fixed Point Theory," Mathematics, MDPI, vol. 11(7), pages 1-15, March.
    4. Xu, Yao & Yu, Jintong & Li, Wenxue & Feng, Jiqiang, 2021. "Global asymptotic stability of fractional-order competitive neural networks with multiple time-varying-delay links," Applied Mathematics and Computation, Elsevier, vol. 389(C).

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