一类食物链模型的Fold-Hopf分支现象分析  

Fold-Hopf Bifurcation Analysis on a Food Chain Model

作　　者：郭爽[1] 张玲[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）》2013年第5期802-806,共5页Journal of Jilin University:Science Edition

基　　金：黑龙江省教育厅科学技术研究项目(批准号:11553003)

摘　　要：对一类Gause型食物链模型,用多项式理论分析了共存平衡点处线性化系统特征方程特征根的分布,给出了产生Fold-Hopf分支的条件.结果表明:该模型存在一个Fold-Hopf分支临界点p=p*,τ=τ0;在(p,τ)参数平面上,该模型出现了拟周期解以及爆发行为等复杂的动力学现象.We employed the polynomial theorem to analyze the distribution of the roots of the associated characteristic equation for the linearized system at the coexisting equilibrium in a Gause- type food chain model. A group of conditions of existence of Fold-Hopf bifurcation were obtained at the coexisting equilibrium. The result indicates that there exists a Fold-Hopf bifurcation point p=p＊ , τ=τ0 in the model. There are complex dynamic behavior such as quasi-periodic motion andbursting behavior on the parameter plane （p,τ）.

关 键 词：Gause型模型 Fold—Hopf分支 拟周期解 爆发行为 

分 类 号：O175.12[理学—数学]