论文标题
循环行为的稳定性在岩纸塞子 - 塞子 - 螺旋杆的杂斜网络模型附近的稳定性
Stability of cycling behaviour near a heteroclinic network model of Rock-Paper-Scissors-Lizard-Spock
论文作者
论文摘要
著名的摇滚乐游戏 - 剪贴器可以用作三个物种之间竞争的简单模型。当使用微分方程在连续时间建模时，所得系统包含三个平衡溶液之间的杂斜周期，代表仅存在一个物种。可以通过增加两种策略（lizard'和`Spock'）以对称方式扩展游戏：现在，每种策略都在其余四种策略中占主导地位，并且由其余两种统治。微分方程模型包含一组耦合的杂斜周期，形成了杂斜网络。在本文中，我们仔细考虑了该异斜网络附近的动态。我们能够识别参数空间的区域，其中任意长期访问的周期序列是对均衡的社区的，在参数空间中形成了复杂的模式。
The well-known game of Rock--Paper--Scissors can be used as a simple model of competition between three species. When modelled in continuous time using differential equations, the resulting system contains a heteroclinic cycle between the three equilibrium solutions representing the existence of only a single species. The game can be extended in a symmetric fashion by the addition of two further strategies (`Lizard' and `Spock'): now each strategy is dominant over two of the remaining four strategies, and is dominated by the remaining two. The differential equation model contains a set of coupled heteroclinic cycles forming a heteroclinic network. In this paper we carefully consider the dynamics near this heteroclinic network. We are able to identify regions of parameter space in which arbitrarily long periodic sequences of visits are made to the neighbourhoods of the equilibria, which form a complicated pattern in parameter space.
