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A finite population destroys a traveling wave in spatial replicator dynamics

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  • Griffin, Christopher
  • Mummah, Riley
  • deForest, Russ

Abstract

We derive both the finite and infinite population spatial replicator dynamics as the fluid limit of a stochastic cellular automaton. The infinite population spatial replicator is identical to the model used by Vickers and our derivation justifies the addition of a diffusion to the replicator. The finite population form generalizes the results by Durett and Levin on finite spatial replicator games. We study the differences in the two equations as they pertain to a one-dimensional rock-paper-scissors game.

Suggested Citation

  • Griffin, Christopher & Mummah, Riley & deForest, Russ, 2021. "A finite population destroys a traveling wave in spatial replicator dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002009
    DOI: 10.1016/j.chaos.2021.110847
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    Cited by:

    1. Griffin, Christopher & Semonsen, Justin & Belmonte, Andrew, 2022. "Generalized Hamiltonian dynamics and chaos in evolutionary games on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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