Behavior of a Competitive System of Second-Order Difference Equations

We study the boundedness and persistence, existence, and uniqueness of positive equilibrium, local and global behavior of positive equilibrium point, and rate of convergence of positive solutions of the following system of rational difference equations: x ( n+1) = (α (1) + β (1) x ( n−1))/(a (1) + b (1) y ( n )), y ( n+1) = (α (2) + β (2) y ( n−1))/(a (2) + b (2) x ( n )), where the parameters α ( i ), β ( i ), a ( i ), and b ( i ) for i ∈ {1,2} and initial conditions x (0), x (−1), y (0), and y (−1) are positive real numbers. Some numerical examples are given to verify our theoretical results.