Deng Bo
Department of Math and Statistics, University of Nebraska, 810 Oldfather Hall, Lincoln, Nebraska 68588-0323.
Chaos. 2001 Sep;11(3):514-525. doi: 10.1063/1.1396340.
Consideration is given to a basic food chain model satisfying the trophic time diversification hypothesis which translates the model into a singularly perturbed system of three time scales. It is demonstrated that in some realistic system parameter region, the model has a unimodal or logistic-like Poincare return map when the singular parameter for the fastest variable is at the limiting value 0. It is also demonstrated that the unimodal map goes through a sequence of period-doubling bifurcations to chaos. The mechanism for the creation of the unimodal criticality is due to the existence of a junction-fold point [B. Deng, J. Math. Biol. 38, 21-78 (1999)]. The fact that junction-fold points are structurally stable and the limiting structures persist gives us a rigorous but dynamical explanation as to why basic food chain dynamics can be chaotic. (c) 2001 American Institute of Physics.
考虑一个满足营养时间多样化假设的基本食物链模型，该假设将模型转化为一个具有三个时间尺度的奇异摄动系统。结果表明，在某些现实的系统参数区域中，当最快变量的奇异参数处于极限值0时，该模型具有单峰或类似逻辑斯谛的庞加莱返回映射。还表明，单峰映射会经历一系列倍周期分岔直至混沌。单峰临界性产生的机制归因于连接折叠点的存在[B. Deng, J. Math. Biol. 38, 21 - 78 (1999)]。连接折叠点结构稳定且极限结构持续存在这一事实，为基本食物链动态为何可能是混沌的提供了一个严格但动态的解释。(c) 2001美国物理研究所。
