Basins of attraction of an anti-competitive discrete rational system

Abstract

We investigate the global asymptotic behavior of solutions of the following anti-competitive system of difference equationswhere the parameters γ1, γ2, β2, A1 are positive numbers and the initial conditions x0 ≥ 0, y0 > 0. We find the basins of attraction of all attractors of the system, which are the equilibrium point and period-two solutions.