Bifurcation and global dynamics of a leslie-gower type Bifurcation and global dynamics of a leslie-gower type competitive system of rational difference equations with competitive system of rational difference equations with quadratic terms quadratic terms
. We investigate global dynamics of the following systems of difference equations 𝑥 𝑛+1 = 𝑥 𝑛 /(𝐴 1 + 𝐵 1 𝑥 𝑛 + 𝐶 1 𝑦 𝑛 ) , 𝑦 𝑛+1 = 𝑦 2𝑛 /(𝐴 2 + 𝐵 2 𝑥 𝑛 + 𝐶 2 𝑦 2𝑛 ) , 𝑛 = 0, 1, .. . , where the parameters 𝐴 1 , 𝐴 2 , 𝐵 1 , 𝐵 2 , 𝐶 1 , and 𝐶 2 are positive numbers and the initial conditions 𝑥 0 and 𝑦 0 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.