Completely integrable replicator dynamics associated to competitive networks
Completely integrable replicator dynamics associated to competitive networks
复制标题
与竞争网络相关的完全可集成的复制动态
DOI：
10.1103/physreve.107.l052202
复制
发表时间：
2023
影响因子：
2.4
通讯作者：
Griffin, Christopher
中科院分区：
文献类型：
--
作者：
Paik, Joshua;Griffin, Christopher
复制方程是演化博弈论中出现的一族常微分方程，与 Lotka-Volterra 密切相关。我们产生了无限族的复制方程，它们是刘维尔-阿诺德可积的。我们通过明确提供守恒量和泊松结构来证明这一点。作为推论，我们将所有锦标赛复制器分类为维度 6 和大部分维度 7。作为一个应用程序，我们展示了 Allesina 和 Levine [Proc.1] 的图 1。国家。阿卡德。科学。 USA 108, 5638 (2011)10.1073/pnas.1014428108] 产生准周期动力学。
The replicator equations are a family of ordinary differential equations that arise in evolutionary game theory, and are closely related to Lotka-Volterra. We produce an infinite family of replicator equations which are Liouville-Arnold integrable. We show this by explicitly providing conserved quantities and a Poisson structure. As a corollary, we classify all tournament replicators up to dimension 6 and most of dimension 7. As an application, we show that Fig. 1 of Allesina and Levine [Proc. Natl. Acad. Sci. USA 108, 5638 (2011)10.1073/pnas.1014428108] produces quasiperiodic dynamics.