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

• Chenyu Liu ^[1] ; Xiaofeng Zhang ^[1]
  1. [1] Beijing Normal University

     Beijing Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.

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