Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.
Graduate School of Science and Technology, Shizuoka University, Hamamatsu 432-8561, Japan.
J Theor Biol. 2018 Dec 7;458:103-110. doi: 10.1016/j.jtbi.2018.09.009. Epub 2018 Sep 11.
Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species.
最近，出现了用于石头剪刀布游戏的复域模型。每个亚群由图上的一个节点表示。个体要么是石头（R），要么是剪刀（S），要么是布（P）；它在亚群之间随机迁移。在本文中，我们假设不同亚群的胜率不同。为了研究每个亚群（节点）的动态状态，我们通过数值方法获得了具有两个和三个节点的图上反应扩散方程的解。在均匀胜率的情况下，我们发现每个亚群都有一个中性稳定的周期解。然而，当亚群之间的胜率不同时，解会趋近于稳定焦点。胜率的异质性促进了物种的共存。
