一类非线性离散人口模型的稳定性和振动性

Asymptotic Stability and Oscillation in a Discrete Population Model with Nonlinearity

目的研究一类非线性离散人口模型的稳定性和振动性．方法采用线性化方法及特征根分析法．结果与结论建立了此模型平衡点稳定的充分性准则，并获得了此模型在一定条件下其正解的渐近性质及其关于正平衡点振动的充分条件，且当ｋ＝０时正平衡点渐近稳定的充分必要性准则是ａ＋ｃｐ２＜２．

Aim To study the dynamics of a discrete population model with nonli nearity. Methods A method of linearization and direct analysis were used. Results and Conclusion Some sufficient as well as sufficient and necessary conditions for the local asymptotic stability of equilibrium points of this model were obtained and some expplicit conditions for its positive solutions to oscillate about its positive equilibrium when a∈,b∈(-∞,∞),c∈(0,∞) were also established.