Stability Analysis of a Prey-Predator Model with Beddington-DeAngelis Functional Response

Abstract

In this paper, a spatial predator-prey system with Beddington - DeAngelis functional response and the modified Leslie - Gower type dynamics under homogeneous Neumann boundary condition is considered. The local and global asymptotic stability of the unique positive homogeneous steady state of the corresponding temporal model are discussed. Moreover, the local stability of the unique constant steady state of the spatiotemporal model is investigated and it is pointed out that spatial patterns cannot occur in the vicinity of this stable steady state.