Stable periodic solutions in a discrete periodic logistic equation

Abstract In this paper, we consider a discrete logistic equation x ( n +1)= x ( n ) exp r ( n ) 1 − x ( n ) K ( n ) where {r(n)} and {K(n)} are positive ω-periodic sequences. Sufficient conditions are obtained for the existence of a positive and globally asymptotically stable ω-periodic solution. Counterexamples are given to illustrate that the conclusions in [1] are incorrect.