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Stability of switched neutral stochastic functional systems with different structures under high nonlinearity

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  • Lu, Boliang
  • Zhu, Quanxin

Abstract

This paper studies the stability of the hybrid neutral stochastic functional differential equations (NSFDEs) with different structures under highly nonlinear conditions. NSFDEs are of wide suitability for simulating random processes with memory, such as tumor evolution mechanism in life science field. The new stochastic system studied in this paper has completely different system structures in different switching subspaces, and the coefficients are highly nonlinear. Moreover, the neutral term is subject to the Markovian switching. This work fills the gap of the stability analysis for differently structured highly nonlinear neutral stochastic functional systems. By using the Lyapunov functional method and the generalized Khasminskii-type conditions, we first establish the existence and uniqueness theorem as well as the asymptotical bounded property of the unique global solution. Then the important stable properties are obtained including H∞ stability, asymptotic stability and exponential stability in Lp. Finally a numerical example is given to illustrate the effectiveness of the results.

Suggested Citation

  • Lu, Boliang & Zhu, Quanxin, 2024. "Stability of switched neutral stochastic functional systems with different structures under high nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    • Handle: RePEc:eee:apmaco:v:475:y:2024:i:c:s0096300324002182
    DOI: 10.1016/j.amc.2024.128746
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    References listed on IDEAS

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    1. Cao, Wenping & Zhu, Quanxin, 2021. "Stability analysis of neutral stochastic delay differential equations via the vector Lyapunov function method," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    2. Mao, Xuerong & Shen, Yi & Yuan, Chenggui, 2008. "Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1385-1406, August.
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    4. Wei Hu, 2018. "A New Stability Criterion for Neutral Stochastic Delay Differential Equations with Markovian Switching," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, October.
    5. Zhengqi Ma & Shoucheng Yuan & Kexin Meng & Shuli Mei, 2023. "Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
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