Local dynamics in a Leslie-Gower system model

Mathematical ecology or/and biology requires the study of populations that interact. This is the reason for the intensive study of the predator-pray models. A Leslie-Gower model of such type is considered here and the stability properties of its equilibrium points are analyticallyand numerically investigated. Dynamics and bifurcations are deduced. Level curves for corresponding Lyapunov functions for various values of the physical parameters in the parameter space are graphically presented emphasizing the stability regions.