Taylor M A, Pavlou S, Kevrekidis I G
Department of Chemical Engineering, Princeton University, New Jersey.
Math Biosci. 1994 Jul;122(1):25-66. doi: 10.1016/0025-5564(94)90081-7.
Predator-prey systems in continuously operated chemostats exhibit sustained oscillations over a wide range of operating conditions. When two such chemostats interact through flow exchange, the interplay of the oscillation frequencies gives rise to a wealth of dynamic behavior patterns. Using numerical bifurcation techniques, we perform a detailed computational study of these patterns and the transitions between them as the coupling strength and relative frequencies of the two chemostats vary. We concentrate on certain strong resonance phenomena between the two frequencies as well as their mutual extinction and provide a representative sampling of possible phase portraits for our model system. Our observations corroborate recent mathematical results and case studies of coupled nonlinear chemical oscillators in which regions of mutual extinction as well as the Arnol'd structure for two-parameter families of maps of the plane have been observed. We highlight certain unexpected features of the operating diagram discovered through our computational study and discuss their implication for the dynamic response of the chemostat system.
在连续运行的恒化器中的捕食者 - 猎物系统在广泛的操作条件下表现出持续振荡。当两个这样的恒化器通过流量交换相互作用时，振荡频率的相互作用会产生丰富的动态行为模式。使用数值分岔技术，我们对这些模式以及当两个恒化器的耦合强度和相对频率变化时它们之间的转变进行了详细的计算研究。我们专注于两个频率之间的某些强共振现象以及它们的相互消失，并为我们的模型系统提供了可能的相图的代表性样本。我们的观察结果证实了最近关于耦合非线性化学振荡器的数学结果和案例研究，其中已经观察到相互消失的区域以及平面映射的双参数族的阿诺尔德结构。我们强调通过计算研究发现的操作图的某些意外特征，并讨论它们对恒化器系统动态响应的影响。
