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

الملخص EN

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 μ.

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 μ, the extinction of P 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.