Stationary distribution of a stochastic reaction–diffusion predator–prey model with additional food, fear effect and anti-predator behavior

Abstract

The stationary distribution, as a fundamental concept in stochastic processes, is of great significance for exploring the long-term behavior and stability of populations. In this paper, a stochastic reaction–diffusion predator–prey model with additional food, fear effect and anti-predator behavior is proposed, in which the stochastic fluctuations are characterized by a Ornstein–Uhlenbeck process. We proved the existence and uniqueness of the stationary distribution of the stochastic model by constructing the Lyapunov function. Moreover, this study extends the work of Qi and Liu (2024).