Stability and bifurcation analysis in a predator prey model involving additive Allee effect

Abstract

In this paper we study codimension 1 Hopf bifurcation for a two dimensional autonomous nonlinear ordinary differential equations system, modeling a predator-prey interaction with Holling type II functional response and additive Allee effect in the prey equation. Positivity, dissipation, boundedness and permanence of the solutions are analyzed. Furthermore, stability and bifurcation analysis are carried out to show the existence of periodic orbits due to the occurrence of codimension 1 Hopf bifurcation, involving weak Allee effect as well as strong Allee effect. In the case of strong Allee effect, through computer simulations carried in MAPLE 13, we conjecture that this model may admit a heteroclinic bifurcation. We present some simulations which allow one to verify the analytical results.

Keywords

• Predator-prey system
• Allee effect
• positivity
• dissipation
• boundedness
• permanence