Cause型捕食模型的稳定性与分支分析  

Stability and Bifurcation Analysis on Gause-Type Predator-Prey Model

作　　者：郭爽[1] 刘洋[1] 沙元霞[1] 于健[1] 

机构地区：[1]大庆师范学院数学科学学院,黑龙江大庆163712

出　　处：《吉林大学学报（理学版）》2012年第5期940-944,共5页Journal of Jilin University:Science Edition

基　　金：黑龙江省普通高校青年学术骨干支持项目(批准号:11251G0011)

摘　　要：用多项式理论分析Gause型捕食模型特征方程特征根的分布规律,给出了共存平衡点稳定及产生Hopf分支的条件.结果表明,该模型存在一个Hopf分支点τ=τ0,使得当0<τ<τ0时,平衡点是局部渐近稳定的;当τ>τ0时,在平衡点附近出现一个稳定的周期解.We used the polynomial theorem to analyze the distribution of the roots of the associated characteris- tic equation for a Gause-type predator-prey model. A group of conditions of stability and the existence of Hopf bifurcation were obtained at the co-existing equilibrium. The result indicates that in the model, there exists a Hopf bifurcation point T = To. The co-existing equilibrium is local asymptotically stable when 0 〈T 〈 To and a stable periodic solution appears near the equilibrium ,point when T〉 To.

关 键 词：Gause型食物链 时滞 稳定性 HOPF分支 

分 类 号：O175.12[理学—数学]