Spatial dynamics of higher order rock-paper-scissors and generalisations

文献类型： 外文期刊

第一作者： Griffin, Christopher

作者： Griffin, Christopher;Feng, Li;Wu, Rongling;Wu, Rongling

作者机构：

关键词： spatial evolutionary dynamics; higher order interactions; travelling waves; replicator dynamics

期刊名称：JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL （ 影响因子：2.1； 五年影响因子：2.0 ）

ISSN： 1751-8113

年卷期： 2024 年 57 卷 18 期

页码：

收录情况： SCI

摘要： We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three strategies (rock-paper-scissors) higher order interaction terms allow travelling waves to emerge in non-declining finite populations. We show that these travelling waves arise from diffusion stabilisation of an unstable interior equilibrium point that is present in the aspatial dynamics. Based on these observations and prior results, we offer two conjectures whose proofs would fully generalise our results to all odd cyclic games, both with and without higher order interactions, assuming a spatial replicator dynamic. Intriguingly, these generalisations for N >= 5 strategies seem to require declining populations, as we show in our discussion.

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