Hopf Bifurcations in Two-Strategy Delayed Replicator Dynamics
Hopf Bifurcations in Two-Strategy Delayed Replicator Dynamics
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DOI：
10.1142/s0218127416500061
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发表时间：
2016-02
期刊：
影响因子：
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通讯作者：
Elizabeth Wesson;R. Rand;David G. Rand
中科院分区：
文献类型：
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作者：
Elizabeth Wesson;R. Rand;David G. Rand
研究了两策略复制子方程的动力学，其中每个策略的适应度是种群频率的函数，延迟时间间隔为T。我们分析了两个模型：在第一个，在适应度的所有条款被延迟，而在第二个，只有相反的策略条款被延迟。我们通过一个线性同伦比较两个模型。以时滞T作为分支参数，我们证明了（非退化）的Hopf分支在这两个模型中的存在，并提出了一个分析所产生的极限环使用Lindstedt的方法。
We investigate the dynamics of two-strategy replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval T. We analyze two models: in the first, all terms in the fitness are delayed, while in the second, only opposite-strategy terms are delayed. We compare the two models via a linear homotopy. Taking the delay T as a bifurcation parameter, we demonstrate the existence of (nondegenerate) Hopf bifurcations in both models, and present an analysis of the resulting limit cycles using Lindstedt’s method.