Linearization, stability, and oscillation of the discrete delayed logistic system

Asymptotic behavior of all solutions of the delayed logistic system x/sub n+1/+ax/sub n/=/spl mu//sub n/x/sub n/(1-x/sub n-/spl sigma//) is investigated. Some sufficient conditions for this equation to be stable are derived, and some necessary and sufficient conditions for oscillations of its solutions are also obtained.