Kuznetsov Y A, Rinaldi S
Dynamical Systems Laboratory, Centrum voor Wiskunde en Informatica, Amsterdam, Netherlands.
Math Biosci. 1996 May;134(1):1-33. doi: 10.1016/0025-5564(95)00104-2.
The main modes of behavior of a food chain model composed of logistic prey and Holling type II predator and superpredator are discussed in this paper. The study is carried out through bifurcation analysis, alternating between a normal form approach and numerical continuation. The two-parameter bifurcation diagram of the model contains Hopf, fold, and transcritical bifurcation curves of equilibria as well as flip, fold, and transcritical bifurcation curves of limit cycles. The appearance of chaos in the model is proved to be related to a Hopf bifurcation and a degenerate homoclinic bifurcation in the prey-predator subsystem. The boundary of the chaotic region is shown to have a very peculiar structure.
本文讨论了由逻辑斯谛食饵、霍林II型捕食者和超级捕食者组成的食物链模型的主要行为模式。该研究通过分岔分析进行，在范式方法和数值延拓之间交替。模型的双参数分岔图包含平衡点的霍普夫、折叠和跨临界分岔曲线以及极限环的翻转、折叠和跨临界分岔曲线。证明了模型中混沌的出现与捕食者-食饵子系统中的霍普夫分岔和退化同宿分岔有关。混沌区域的边界显示出非常奇特的结构。
