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Games 2016, 7(3), 24; doi:10.3390/g7030024

The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games

Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
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Academic Editor: Attila Szolnoki
Received: 5 August 2016 / Accepted: 31 August 2016 / Published: 9 September 2016
(This article belongs to the Special Issue Evolutionary Games and Statistical Physics of Social Networks)
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Abstract

We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance (dominance-removal and dominance-replacement), mutations, and pair-exchange of neighboring individuals. Here, we study the influence of mobility on the emerging patterns and investigate when the pair-exchange rate is responsible for spiral waves to become elusive in stochastic lattice simulations. In particular, we show that the spiral waves predicted by the system’s deterministic partial equations are found in lattice simulations only within a finite range of the mobility rate. We also report that in the absence of mutations and dominance-replacement, the resulting spiraling patterns are subject to convective instability and far-field breakup at low mobility rate. Possible applications of these resolution and far-field breakup phenomena are discussed. View Full-Text
Keywords: Rock-Paper-Scissors; cyclic dominance; pattern formation; spiral waves; diffusion; phase diagram; individual-based modelling; stochastic lattice simulations; complex Ginzburg-Landau equation Rock-Paper-Scissors; cyclic dominance; pattern formation; spiral waves; diffusion; phase diagram; individual-based modelling; stochastic lattice simulations; complex Ginzburg-Landau equation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Mobilia, M.; Rucklidge, A.M.; Szczesny, B. The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games. Games 2016, 7, 24.

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