Dynamics of a Two-Dimensional Cooperative System of Polynomial Difference Equations With Cubic Terms - Bektešević, Jasmin; Hadžiabdić, Vahidin; Mehuljić, Midhat; Mujić, Naida (Sarajevo Journal of Mathematics, 2024)
In this paper we present a local dynamics and investigate the global behavior of the following system of difference equations x_n+1=ax_n^3+by_n^3 y_n+1=Ax_n^3+By_n^3 nN_0 with non-negative parameters and initial conditions x_0 and y_0 that are real numbers. We establish the relations for local stability of equilibriums and necessary and sufficient conditions for the existence of period-two solution(s). We then use this result to give global behavior results for special ranges of parameters and determine the basins of attraction of all equilibrium points.