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Mean Square Stability of Impulsive Stochastic Delayed Reaction-Diffusion Equations via Comparison Principle with Razumikhin Method

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Abstract

This paper investigates the mean square stability problem for impulsive stochastic delayed reaction-diffusion equations. By employing stochastic analysis theory, impulsive differential inequality technique and Razumikhin method, comparison principle for impulsive stochastic delayed reaction-diffusion equations is firstly established. Then, by using the comparison principle, some sufficient conditions are derived to ensure the mean square stability, mean square uniform stability, mean square asymptotic stability and mean square exponential stability of such systems. Finally, an example is provided to show the effectiveness of the proposed results.

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Authors and Affiliations

  1. College of Mathematics Science, Sichuan Normal University, Chengdu, 610066, China

    Zhao Li

  2. School of Mathematics and Physics, Mianyang Teachers’ College, Mianyang, 621000, China

    Shuyong Li

Authors
  1. Zhao Li
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  2. Shuyong Li
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Correspondence to Shuyong Li.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11571245.

This paper was recommended for publication by Editor SUN Jian.

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Li, Z., Li, S. Mean Square Stability of Impulsive Stochastic Delayed Reaction-Diffusion Equations via Comparison Principle with Razumikhin Method. J Syst Sci Complex 33, 1012–1022 (2020). https://doi.org/10.1007/s11424-020-8353-3

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  • DOI: https://doi.org/10.1007/s11424-020-8353-3

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