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.
Wang et al. (Thu,) studied this question.
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