Global dynamics of a rational system of difference equations in the plane

Abstract

We investigate the global stability properties and asymptotic behavior of solutions of the system of difference equations Xn+1 = Xn/a+Yn2, Yn+1 = Yn/b+Xn2, n = 0, 1,... where the parameters a and b are positive numbers, and the initial conditions x0 and y0 are arbitrary nonnegative numbers