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Stability of stochastic McKean–Vlasov differential equations with impulses
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DOI：10.1002/asjc.70156.png)
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Abstract
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This paper focuses on the stability analysis of impulsive stochastic McKean–Vlasov differential equations (ISMVDEs). The impulsive dynamics introduced in this study have not been widely explored in the existing literature on stochastic McKean–Vlasov differential equations (SMVDEs). This study provides a novel research perspective for such equations and enables their application to more complex scenarios. We first relax the traditional Lyapunov conditions for stability analysis in probability. Different from previous studies that assumed the generator to be negative-definite, we demonstrate that this condition can be relaxed, thus allowing the analysis of a broader class of systems. Furthermore, based on the Mean Dwell Time (MDT) and Reverse Mean Dwell Time (RMDT) conditions, we construct a comprehensive framework to evaluate the mean exponential stability. This framework is proven to be an effective tool for analyzing both stable and unstable impulses, offering a more meticulous stability analysis for systems with complex dynamics. A practical example is provided to validate the applicability of the theoretical results. The methods proposed in this work make significant contributions to the understanding of ISMVDEs and provide powerful tools for analyzing and controlling the stability of complex dynamic systems.
Keywords:
impulsive stochastic system
mean-square exponential stability
stochastic McKean–Vlasov differential equation
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