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

Providing additional food supplements to predators is one of the crucial and effective tools for biological conservation and pest management, which has been widely recognized and validated by theoretical and experimental scientists. This paper focuses on the existence and uniqueness of stationary distribution of a stochastic reaction-diffusion predator-prey model that incorporates additional food for predator and fear effect for prey. It reveals that spatial diffusion is beneficial for maintaining the steady state of the model, whereas environment white noise has a negative effect.