An Example of a Globally Asymptotically Stable Anti-monotonic System of Rational Difference Equations in the Plane - Burgić, Dževad; Nurkanović, Zehra (Sarajevo Journal of Mathematics, 2024)
We consider the following system of rational difference equations in the plane: { aligned%rcl x_n+1 &= α_1A_1+B_1 x_n+ C_1y_n [0.2cm] y_n+1 &= α_2A_2+B_2 x_n+ C_2y_n aligned . , n=0,1,2,… where the parameters α_1, α_2, A_1, A_2, B_1, B_2, C_1, C_2 are positive numbers and initial conditions x_0 and y_0 are nonnegative numbers. We prove that the unique positive equilibrium of this system is globally asymptotically stable. Also, we determine the rate of convergence of a solution that converges to the equilibrium E=(x,y) of this systems. 2000 Mathematics Subject Classification. 39A10, 39A11, 39A20