<p>For stochastic delayed systems, the stochastic ultimate boundedness of solutions has always been a property of significant importance. This paper focuses on investigating a stochastic delayed food chain chemostat model. First, the existence and uniqueness of a global positive solution for the model are established. Subsequently, by constructing an appropriate Lyapunov functional and applying Chebyshev’s inequality, we further prove that the positive solution is stochastically ultimately bounded. This study provides a theoretical foundation and methodological reference for the stability analysis of stochastic delayed biological dynamical systems.</p>

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Analysis on the Ultimate Boundedness of Solutions for Stochastic Delayed Food-Chain Chemostat Model

  • Chenyu Liu,
  • Xiaofeng Zhang

摘要

For stochastic delayed systems, the stochastic ultimate boundedness of solutions has always been a property of significant importance. This paper focuses on investigating a stochastic delayed food chain chemostat model. First, the existence and uniqueness of a global positive solution for the model are established. Subsequently, by constructing an appropriate Lyapunov functional and applying Chebyshev’s inequality, we further prove that the positive solution is stochastically ultimately bounded. This study provides a theoretical foundation and methodological reference for the stability analysis of stochastic delayed biological dynamical systems.