Stability of a Leslie-Gower type predator-prey model with a strong Allee effect with delay

Abstract

In this paper, a modified Leslie-Gower type predator-prey model introducing in prey population growth a delayed strong Allee effect is studied. The Leslie-Gower model with Allee effect has none, one or two positive equilibrium points but the incorporation of a time delay in the growth rate destabilizes the system, breaking the stability when the delay cross a critical point. The existence of a Hopf bifurcation is studied in detail and the numerical simulations confirm the theoretical results showing the different scenarios. We present biological interpretations for species prey-predator type.

Keywords

• allee effect
• leslie-gower predator-prey model
• delay parameter
• stability
• hopf bifurcation