Dynamics of a Second-order System of Nonlinear Difference Equations

Abstract

In this paper, we investigate the equilibrium points, stability of two equilibrium points, convergences of negative equilibrium point, periodic solutions, and existence of bounded or unbounded solutions of a system of nonlinear difference equations x(n+1) = x(n-1)y(n) - 1, y(n+1) = y(n-1)x(n) - 1 n = 0, 1,..., where the initial values are real numbers. Additionally we present some numerical examples to verify our theoretical results.