Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical Networks

Takashi Nagatani and Genki Ichinose

Complexity, 2020, vol. 2020, 1-8

Abstract:

We present a metapopulation dynamic model for the diffusively-coupled rock-paper-scissors (RPS) game with mutation in scale-free hierarchical networks. We investigate how the RPS game changes by mutation in scale-free networks. Only the mutation from rock to scissors ( R -to- S ) occurs with rate . In the network, a node represents a patch where the RPS game is performed. RPS individuals migrate among nodes by diffusion. The dynamics are represented by the reaction-diffusion equations with the recursion formula. We study where and how species coexist or go extinct in the scale-free network. We numerically obtained the solutions for the metapopulation dynamics and derived the transition points. The results show that, with increasing mutation rate , the extinction of species occurs and then the extinction of R species occurs, and finally only S species survives. Thus, the first and second dynamical phase transitions occur in the scale-free hierarchical network. We also show that the scaling law holds for the population dynamics which suggests that the transition points approach zero in the limit of infinite size.

Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:6976328

DOI: 10.1155/2020/6976328

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