Effects of Random Diffusion and Advection on a Predator–Prey Model

ABSTRACT In this article, we investigate the steady state problem of a predator–prey model incorporating random diffusion and advection under homogeneous Dirichlet boundary conditions. To gain a better understanding of random diffusion and advection, the stability of semitrivial steady state solutions, the nonexistence and existence of positive steady‐state solutions are given. The results indicate that diffusion has a significant influence on both the stability of semitrivial steady state solutions and the coexistence region. In particular, a small positive advection coefficient reduces the size of the coexistence region, whereas a large positive advection coefficient may lead to bistable phenomena. Moreover, as other parameters vary, the stability of one semitrivial steady state solution may change at least twice.