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We investigate global dynamics of the following systems of difference equations xn+1=xn/A1+B1xn+C1yn, yn+1=yn2/A2+B2xn+C2yn2, 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.

Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms