Higher-order dynamics in the replicator equation produce a limit cycle in rock-paper-scissors
Higher-order dynamics in the replicator equation produce a limit cycle in rock-paper-scissors
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DOI：
10.1209/0295-5075/accd93
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发表时间：
2023-01
期刊：
影响因子：
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通讯作者：
Christopher H. Griffin;R. Wu
中科院分区：
文献类型：
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作者：
Christopher H. Griffin;R. Wu
最近的研究表明，成对的相互作用可能不足以完全模拟野外的生态动态。在这封信中，我们考虑一个复制动力学，考虑两两和三元相互作用使用秩三张量。我们研究这些新的非线性动力学使用广义的石头剪刀布游戏，其动力学是很好地理解在标准的复制意义。我们发现，除了高阶动力学导致创建一个亚临界的霍普夫分岔，因此一个不稳定的极限环。众所周知，这种行为不会发生在任何三策略博弈中的成对复制子中，这表明高阶相互作用可以对系统的动态产生影响。我们数值表征参数制度中存在的极限环，并讨论了可能的方法来推广这种方法来研究高阶相互作用。
Recent work has shown that pairwise interactions may not be sufficient to fully model ecological dynamics in the wild. In this letter, we consider a replicator dynamic that takes both pairwise and triadic interactions into consideration using a rank-three tensor. We study these new nonlinear dynamics using a generalized rock-paper-scissors game whose dynamics are well understood in the standard replicator sense. We show that the addition of higher-order dynamics leads to the creation of a subcritical Hopf bifurcation and consequently an unstable limit cycle. It is known that this kind of behaviour cannot occur in the pairwise replicator in any three-strategy games, showing the effect higher-order interactions can have on the resulting dynamics of the system. We numerically characterize parameter regimes in which limit cycles exist and discuss possible ways to generalize this approach to studying higher-order interactions.