A Difference Equation Arising from Logistic Population Growth

摘要

Let k ∈ Z{sub}+ = {0, 1, 2, ...... } be a fixed nonnegative integer, In this article we investigate the boundedness and the global attractivity of the positive solutions of the difference equation x{sub}(n+k+1) = (α+βx{sub}n)/(1+g(x{sub}(n+k))), n∈Z{sub}+， with 0 ≤ α, β ≤ ∞. Here g is a real continuous function and initial conditions, X{sub}0, x{sub}1, ......, x{sub}k are nonnegative real numbers.