Dynamics of a family of two-dimensional difference systems

The boundedness and global asymptotic behavior of positive solutions of the nonlinear two-dimensional difference systems xn=Φ(xn-t1,yn-s1),yn=Ψ(yn-s2,xn-t2), where t1,s1,s2,t2t1,s1,s2,t2 are all positive integers, are investigated. Some sufficient conditions are established such that the positive solutions converge to the unique equilibrium. Finally, some examples are given to illustrate our results.