同宿轨道
博格达诺夫-塔肯分岔
数学
霍普夫分叉
余维数
同宿分支
分叉
通才与专种
分岔图
跨临界分岔
应用数学
纯数学
物理
生态学
生物
栖息地
量子力学
非线性系统
作者
Gunog Seo,Gail S. K. Wolkowicz
出处
期刊:Discrete and Continuous Dynamical Systems - Series S
[American Institute of Mathematical Sciences]
日期:2020-01-01
卷期号:13 (11): 3157-3187
被引量:8
标识
DOI:10.3934/dcdss.2020163
摘要
Magal et al. [13] studied both spatial and non-spatial host-parasitoid models motivated by biological control of horse-chestnut leaf miners that have spread through Europe. In the non-spatial model, they considered pest control by predation of leaf miners by a generalist parasitoid with a Holling type II functional (Monod) response. They showed that there can be at most six equilibrium points and discussed local stability. We revisit their model in the non-spatial case, identify cases missed in their investigation and discuss consequences for possible pest control strategies. Both the local stability of equilibria and global properties are considered. We use a bifurcation theoretical approach and provide analytical expressions for fold and Hopf bifurcations and for the criticality of the Hopf bifurcations. Our numerical results show very interesting dynamics resulting from codimension one bifurcations including: Hopf, fold, transcritical, cyclic-fold, and homoclinic bifurcations as well as codimension two bifurcations including: Bautin and Bogdanov-Takens bifurcations, and a codimension three Bogdanov-Takens bifurcation.
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