Dynamics of a fourth-order system of rational difference equations

In this paper, we study the equilibrium points, local asymptotic stability of an equilibrium point, instability of equilibrium points, periodicity behavior of positive solutions, and global character of an equilibrium point of a fourth-order system of rational difference equations of the form x(n+1) = alpha x(n-3)/beta + gamma y(n)y(n-1)y(n-2)y(n-3), y(n+1) = alpha(1)y(n-3)/beta(1) + gamma(1)x(n)x(n-1)x(n-2)x(n-3), n = 0,1, ... , where the parameters alpha, beta,gamma, alpha(1), beta(1), gamma(1) and initial conditions x(0), x(-1), x(-2), x(-3), y(0), y(-1), y(-2), y(-3) are positive real numbers. Some numerical examples are given to verify our theoretical results.