Dynamics Behavior of Stochastic Chemostat Model With Reaction–Diffusion

This paper investigates the dynamic behavior of a stochastic chemostat model with reaction–diffusion. Prior studies predominantly explored system dynamics using the basic reproduction number. However, we examine the system's persistence and extinction from an alternative standpoint, focusing on the conditions determined by coefficient relationships. We establish the dynamical behavior of the system by constructing Lyapunov functions and employing a semigroup approach. Numerical simulations confirm the theorem's results based on coefficient relationships.