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This article aims to investigate sufficient conditions for the stability ofstochastic differential equations with a random structure, particularly incontexts involving the presence of concentration points. The proof ofasymptotic stability leverages the use of Lyapunov functions, supplemented byadditional constraints on the magnitudes of jumps and jump times, as well asthe Markov property of the system solutions. The findings are elucidated withan example, demonstrating both stable and unstable conditions of the system.

Stability of stochastic dynamic systems of a random structure with Markov switchings in the presence of concentration points