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.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
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)
