AI 中文总结
探讨W. Semmler和M. Sieveking提出的流动性增长聚合模型中的极限环问题，修改模型纳入弱阿利效应，借助霍普夫-安德罗诺夫理论研究局部分岔，动机源于经济理论，该效应在数学生态学中也有类似重要性。
AI 中文摘要
我们讨论了W. Semmler和M. Sieveking在文献中提出并从理论和数值上研究的流动性增长聚合模型中的极限环问题。他们的模型局部属于捕食者-猎物类型，捕食者（利润）存在自相残杀，猎物（流动性）种群有逻辑斯蒂边界。我们修改模型以纳入流动性的弱阿利效应，并借助霍普夫-安德罗诺夫理论研究平衡点和极限环的局部分岔。本研究的主要动机源于Leijonhuvud在文献中引入的所谓稳定走廊的经济理论。然而，这些效应在生物学中最初发展的动力学模型，特别是数学生态学中也具有类似的重要性。
英文摘要
We discuss the problem of limit cycles in an aggregate-type models of liquidity growth proposed and studied both theoretically and numerically by W. Semmler and M. Sieveking in \cite{SemmlerSieveking}. Their model is locally of predator-prey type with cannibalism in predator (profit) and logistic bound on prey's population (liquidity). We modify the model to include the weak Allee effect in liquidity and to study the local bifurcations of equilibria and limit cycles by means of the Hopf-Andronov theory. The main motivation for this study follows the economic theory of the so-called corridors of stability introduced by Leijonhuvud in \cite{Leijonh}. Similar importance of these effects is, however, found also in the originally developed dynamical models in biology, especially in mathematical ecology.
