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Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach

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  • Yonggui Kao
  • Hamid Reza Karimi

Abstract

This paper is devoted to investigating stability in mean of partial variables for coupled stochastic reaction-diffusion systems on networks (CSRDSNs). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations (SODE) and using Itô formula, we establish some novel stability principles for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, and exponential stability in mean of partial variables for CSRDSNs. These stability principles have a close relation with the topology property of the network. We also provide a systematic method for constructing global Lyapunov function for these CSRDSNs by using graph theory. The new method can help to analyze the dynamics of complex networks. An example is presented to illustrate the effectiveness and efficiency of the obtained results.

Suggested Citation

  • Yonggui Kao & Hamid Reza Karimi, 2014. "Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, May.
    • Handle: RePEc:hin:jnlaaa:597502
    DOI: 10.1155/2014/597502
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    Cited by:

    1. Zhang, Caihong & Kao, Yonggui & Kao, Binghua & Zhang, Tiezhu, 2018. "Stability of Markovian jump stochastic parabolic Itô equations with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 399-407.
    2. Tao, Ruifeng & Ma, Yuechao & Wang, Chunjiao, 2020. "Stochastic admissibility of singular Markov jump systems with time-delay via sliding mode approach," Applied Mathematics and Computation, Elsevier, vol. 380(C).

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