论文标题
在捕食者捕食系统中，多个极限循环和杂斜循环在猎物中具有质量影响
Multiple Limit Cycles and Heteroclinic Loops in a Predator-prey System with Allee Effects in Prey
论文作者
论文摘要
猎物中强与弱的效果之间的过渡提供了生态学的简单政权转变。恶化的环境会将弱的效果变成强大的效果。在本文中，我们研究了Holling IV型的功能响应与强和弱的效果之间的功能响应之间的相互作用。此处研究的模型列出了复杂的动力学和高的编构分叉。特别地，完全分析了nilpotent尖叉分叉，nilpotent鞍形分叉和退化的hopf分叉3，并且被完全分析，并且存在同质和异斜循环的存在。值得注意的是，这是第一次在具有Allee效应的捕食者捕食模型中发现三个极限周期。事实证明，强大的质量影响破坏了人口动态的稳定，引起更多的政权转移，减少了这两种物种的可能性，增加了生态系统崩溃的脆弱性，而弱的耕作效应促进了与无股东效应的系统相比，捕食者和猎物之间的持续振荡。此处开发的理论为理解自然系统中物种的捕食者 - 捕获相互作用和生物多样性提供了合理的基础。
The transition between strong and weak Allee effects in prey provides a simple regime shift in ecology. A deteriorating environment changes weak Allee effects into strong ones. In this paper, we study the interplay between the functional response of Holling type IV and both strong and weak Allee effects. The model investigated here presents complex dynamics and high codimension bifurcations. In particular, nilpotent cusp bifurcation, nilpotent saddle bifurcation and degenerate Hopf bifurcation of codimension 3 are completely analyzed, and the existence of homoclinic and heteroclinic loops are proven. Remarkably it is the first time that three limit cycles are discovered in predator-prey models with Allee effects. It turns out that strong Allee effects destabilize population dynamics, induce more regime shifts, decrease establishment likelihood of both species, increase vulnerability of ecosystem to collapse, while weak Allee effects promote sustained oscillations between predators and preys compared to systems without Allee effects. The theory developed here provides a sound foundation for understanding predator-prey interactions and biodiversity of species in natural systems.
