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

Mauro Mobilia, Alastair M. Rucklidge and Bartosz Szczesny
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Mauro Mobilia: Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
Alastair M. Rucklidge: Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
Bartosz Szczesny: Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK

Games, 2016, vol. 7, issue 3, 1-12

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.

Keywords: Rock-Paper-Scissors; cyclic dominance; pattern formation; spiral waves; diffusion; phase diagram; individual-based modelling; stochastic lattice simulations; complex Ginzburg-Landau equation (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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