Stability analysis of a Lotka-Volterra type predator-prey system with Allee effect on the predator species

Abstract

In this paper, we propose a Lotka-Volterra type predator-prey system with Allee effect on the predator species. Sufficient condition which ensure the existence of a unique globally asymptotically stable positive equilibrium is obtained. Numeric simulation s show that the system subject to an Allee effect takes much longer time to reach its stable steady-state solution, however, Allee effect has no influence on the final density of the predator and prey species. This result differs from that obtained for the predator prey system with Allee effect on the prey species.