Bifurcation and global dynamics of a leslie-gower type competitive system of rational difference equations with quadratic terms

Abstract

We investigate global dynamics of the following systems of difference equations xn+1 = xn/(A1 + B1xn + C1yn), yn+1+1 = yn2/(A2 + B2xn + C2ynP), n = 0, 1, ., where the parameters A1, A2, B1, B2, C1, and C2 are positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers.This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space.