Dynamics of a diffusive prey-predator system with strong allee effect growth rate and a protection zone for the prey

Abstract

In this paper, a diffusive prey-predator model with strong Allee effect growth rate and a protection zone Ω0 for the prey is investigated. We analyze the global existence, long time behaviors of positive solutions and the local stabilities of semi-trivial solutions. Moreover, the conditions of the occurrence and avoidance of overexploitation phenomenon are obtained. Furthermore, we demonstrate that the existence and stability of non-constant steady state solutions branching from constant semi-trivial solutions by using bifurcation theory. Our results show that the protection zone is effective when Allee threshold is small and the protection zone is large.