AI 中文总结
研究具有广义捕食者竞争和Holling II型功能反应的额外食物模型，发现其有复杂分岔结构，包括至少4维（或3维）的尖点型（或焦点型）Bogdanov - Takens分岔、3维的全局Hopf分岔和3维的同宿分岔，证明额外食物可增强Bazykin型模型分岔结构，对虫害管理有启示。
AI 中文摘要
额外食物来源和捕食者竞争都会影响捕食者 - 猎物模型的动态。具有Holling II型功能反应的Bazykin捕食者竞争模型有丰富的分岔结构。额外食物模型能降低害虫数量。本文研究了具有广义捕食者竞争和Holling II型功能反应的额外食物模型，发现其根据参数值可有多达三个内部平衡点，还展示了至少4维（或3维）的尖点型（或焦点型）Bogdanov - Takens分岔、3维的全局Hopf分岔和3维的同宿分岔，表明在BT点周围可能存在三个极限环。结果证明额外食物可增强Bazykin型模型的分岔结构，并讨论了对大豆蚜虫综合虫害管理计划的适用性，结果表明额外食物生物防治是入侵害虫的有效管理策略。
英文摘要
Additional food sources and predator competition are both known to impact the dynamics of predator-prey models. The Bazykin model of predator competition, with Holling type II functional response, possesses a rich bifurcation structure consisting of a focus-type degenerate Bogdanov-Takens bifurcation of codimension 3, and a degenerate Hopf bifurcation of codimension at most 2. Additional food models on the other hand are able to drive pest populations lower, with vast applicability in biological control. Despite these models being studied rigorously in the literature, the global bifurcation structure, of their possible complex dynamics, in a unified model, is unknown. In this work, we study an additional food model with generalized predator competition and Holling type-II functional response. Depending on the parameter values, the system can have up to three interior equilibria. Further, we show that this system exhibits a cusp-type (or focus-type) Bogdanov-Takens bifurcation of codimension at least 4 (or 3), a global Hopf bifurcation of codimension 3, and a homoclinic bifurcation of codimension 3. This shows there could exist three limit cycles around the BT point. These results demonstrate that additional food in Bazykin type models, can enhance their bifurcation structure. We discuss the applicability of these results to integrated pest management programs for the soybean aphid, wherein long term field data in the North-Central United States, shows two distinct limit cycles in aphid populations and their predators. Our results suggest biological control with additional food, is an effective management tactic for invasive pests.
Comments54 pages, 24 figures
