A CLASS OF LESLIE-GOWER TYPE PREDATOR-PREY MODEL WITH SIGMOID FUNCTIONAL RESPONSE

Abstract

This work deals with a continuous-time predator-prey model of Leslie-Gower type considering a Holling III type functional response. Conditions for the existence of equilibrium points, their local stability and the existence of at least one limit cycle in the phase plane are established In particular we show that the point t (0; 0) has a great importance on the dynamics of model, since it has a separatrix curve dividing the behavior of trajectories. Those upper this curve have the point (0; 0) as their ! ? limit. So, the extinction of both populations can be possible according to the initial conditions.