Stability in a population model

摘要

Consider the difference equation ξn+1 = αξn + βξn1+ξn−k, n=0,1,…, where 0 ⩽ α < α < 1 < α + β, γ∈(0,∞) and k∈{0,1…}, When k = 0, (∗) was proposed by Milton and Belar as a model for the bobwhite quail population of northern Wisconsin. In this paper, we investigate the stability properties of (∗) and establish some sufficient conditions for the positive equilibrium of (∗) to be globally asymptotically stable.