Asymptotic behavior of delay 2-D discrete logistic systems

Asymptotic behavior of all solutions of the delay two-dimensional logistic system x/sub m+1,/ /sub n/+ax/sub m,/ /sub n+1/=/spl mu//sub mn/x/sub mn/ (1-x/sub m-/spl sigma/, n-/spl tau//) is investigated. Some sufficient conditions for the stability of this equation are derived. Moreover, some sufficient and necessary conditions for oscillations of all solutions of this equation are obtained.