Stochastic Dynamics and Density Function of a Food Chain Model with Infinite Distributed Delay

Abstract

This paper explores a stochastic three-species food chain model with infinite distributed delay. By the linear chain technique, the model is transformed into a new higher-dimensional stochastic differential equation. First, the existence and uniqueness of the global positive solution to the model is proved, as well as the boundedness of the moments of the solution. Then, sufficient conditions for the global attractivity of the system are obtained. Next, we derive an explicit analytical expression for the probability density function of the system around the quasi-positive equilibrium. Finally, we provide some numerical examples to verify the validity of the results.