TY - JOUR
T1 - A finite population destroys a traveling wave in spatial replicator dynamics
AU - Griffin, Christopher
AU - Mummah, Riley
AU - deForest, Russ
N1 - Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2021/5
Y1 - 2021/5
N2 - 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.
AB - 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.
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U2 - 10.1016/j.chaos.2021.110847
DO - 10.1016/j.chaos.2021.110847
M3 - Article
AN - SCOPUS:85103640423
SN - 0960-0779
VL - 146
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 110847
ER -