Dynamics of a reaction–diffusion three-species food chain model: Effect of space-time white noise

Abstract

This paper is devoted to analyzing the influence of space-time white noise on the dynamics of biological mathematical models in spatiotemporal scenarios based on stochastic partial differential equations (SPDEs). Here, we propose a stochastic reaction–diffusion three-species food chain model with various functional response functions. The motivation of the SPDEs model construction is mainly twofold: (1) when species migrate in space, space-time white noise is a factor that cannot be ignored; (2) functional response function is an essential indicator for directly measuring the relationship between species in biological mathematical models. To discuss the long-term behaviors of the SPDEs model in spatial heterogeneous environment, we first analyze the well-posedness of mild and strong solutions, respectively. Then, the critical conditions for determining the permanence and extinction of populations are given, which reveal that high-intensity white noise can lead to the extinction of predator populations. The validity of the theoretical results is also performed by numerical simulation. In particular, this new theoretical method may be extended to the study of other stochastic biological mathematical models in spatiotemporal scenarios, such as eco-epidemiological models, high-dimensional population models and epidemic models.