四维Lotka-Volterra竞争模型的异宿环以及Hopf分岔分析  

Heteroclinic loop and Hopf bifurcation analysis of a four-dimensional Lotka-Volterra competition model

作　　者：贾安凡 孙伟刚[1] JIA Anfan;SUN Weigang(School of Sciences,Hangzhou Dianzi University,Hangzhou 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）》2024年第3期72-78,共7页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(61673144)。

摘　　要：Lotka-Volterra竞争模型的瞬态动力学与异宿环结构密切相关,同时对理解物种之间相互竞争的无赢家竞争现象起着重要的作用。为了研究Lotka-Volterra竞争模型的异宿环拓扑结构,通过设计Matlab程序确定了四维模型的系统参数;在此参数下发现系统的异宿环由四个鞍点构成,并且在异宿环外部存在一个极限环;利用Routh-Hurwitz判据和Poincare规范形理论对极限环的稳定性进行了理论分析。The transient dynamics of the Lotka-Volterra competition model are closely associated with the presence of heteroclinic cycles,which plays a vital role in understanding the phenomenon of non-transitive competition among species.To investigate the heteroclinic cycle topology of the Lotka-Volterra competition model,a Matlab program is designed to determine the system parameters of the four-dimensional model.Under these parameters,it is discovered that the system's heteroclinic cycle is composed of four saddle points,with an outer limit cycle existing outside the heteroclinic cycle.The stability of the limit cycle is theoretically analyzed by using the Routh-Hurwitz criterion and the Poincare normal form theory.

关 键 词：异宿环 极限环 HOPF分岔 Poincare规范形 

分 类 号：O175.14[理学—数学]