两种群竞争系统离散等级结构模型分析  

Analysis for discrete hierarchical model of two-species competing system

作　　者：谷思源 何泽荣[1] GU Siyuan;HE Zerong(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2022年第4期83-87,共5页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(11871185)。

摘　　要：研究一类具有离散等级结构的两种群竞争系统模型。首先,证明了解的有界性;然后,定义了两种群的基本再生数,并分析了正平衡态的存在性;接着,运用本原矩阵的特征值理论导出零平衡态的稳定性条件;最后,通过构造Lyapunov函数,获得了全局稳定性判据。This paper is concerned with a class of nonlinear two-species competition model with discrete hierarchical structure.Firstly,the boundedness of the solutions is proved.Secondly,the formulae of the basic reproductive numbers for two populations are defined,and the existence of positive steady states is analyzed.Thirdly,the linear stability conditions of the zero state are obtained by means of the eigenvalue theory of the primitive matrices.Finally,the global stability of the zero state is established by a Lyapunov function.

关 键 词：等级结构 竞争关系 稳定性 非负矩阵 LYAPUNOV函数 

分 类 号：O241.84[理学—计算数学]