A note on the stationary distribution of a three-species food web stochastic model with generalist predator.

In this paper, a three-species food web stochastic model with generalist predator is proposed and studied. We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological viewpoint, the existence of a stationary distribution implies that all species can coexist in a community. • A three-species food web stochastic model with generalist predator is studied. • We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution. • The existence of a stationary distribution implies that all species can coexist in a community. [ABSTRACT FROM AUTHOR]