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Pest control by generalist parasitoids: A bifurcation theory approach
Discrete and Continuous Dynamical Systems-Series S ( IF 1.8 ) Pub Date : 2019-12-06 , DOI: 10.3934/dcdss.2020163 Gunog Seo , , Gail S. K. Wolkowicz ,
Discrete and Continuous Dynamical Systems-Series S ( IF 1.8 ) Pub Date : 2019-12-06 , DOI: 10.3934/dcdss.2020163 Gunog Seo , , Gail S. K. Wolkowicz ,
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.
中文翻译:
通才寄生虫控制害虫:分叉理论方法
Magal等。[13 ]研究了在欧洲范围内传播的七叶树栗矿工的生物控制所激发的空间和非空间寄主寄生虫模型。在非空间模型中,他们考虑了通过具有Holling II型功能(Monod)响应的通才寄生虫捕食矿工来控制害虫。他们表明最多可以有六个平衡点,并讨论了局部稳定性。我们在非空间案例中重新研究他们的模型,确定在调查中遗漏的案例,并讨论可能的有害生物控制策略的后果。平衡的局部稳定性和整体性质都被考虑。我们使用分叉理论方法,并提供了折叠和Hopf分叉以及Hopf分叉的临界性的解析表达式。
更新日期:2019-12-06
中文翻译:
通才寄生虫控制害虫:分叉理论方法
Magal等。[