论文标题
与竞争性网络相关的完全可集成的复制器动力学
Completely Integrable Replicator Dynamics Associated to Competitive Networks
论文作者
论文摘要
复制器方程是进化游戏理论中出现的普通微分方程家族，与Lotka-Volterra密切相关。我们生产一个无限的复制器方程家族，这些方程式是liouville-arnold。我们通过明确提供保守的数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尺寸6和大部分维度。作为应用程序，我们表明``Allesina and Levine of``竞赛网络的物种多样性网络理论''（Proc。Natl。Acad。Sci。，2011年）产生了Quasiperiodic Dynamics。
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 ``A competitive network theory of species diversity" by Allesina and Levine (Proc. Natl. Acad. Sci., 2011), produces quasiperiodic dynamics.
