Spatiotemporal dynamics of a predator-prey system with Beddington-DeAngelis functional response and the modified Leslie-Gower type dynamics incorporating prey refuge

Abstract

In this paper, a spatial predator-prey system with Beddington-DeAngelis functional response and the modified Leslie-Gower type dynamics incorporating constant proportion of prey refuge under homogeneous Neumann boundary condition is considered. The qualitative properties, including the persistence property, local and global asymptotic stability of the unique positive homogeneous steady state are discussed. Furthermore, a series of numerical simulations are performed and the results of the numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripe like or spotted or coexistence of both. The results indicate that the effect of the prey refuge for pattern formation is remarkable. More specifically, as the value of the prey refuge constant is increased, the stripe like patterns breaks down and ultimately form spotted like patterns.