Stability and Bifurcation in a Second-Order Difference System

Abstract

In the paper, we examine the system

                                                                                             (1)

where  are positive real numbers and the initial conditions  are arbitrary nonnegative numbers. We investigate the persistence, boundedness, convergence, invariance, and global asymptotic character of the positive solutions of (1). Bifurcation diagrams are then plotted to visualize the periodic character.