Mobilia, M, Rucklidge, AM orcid.org/0000-0003-2985-0976 and Szczesny, B (2016) The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games. Games, 7 (3). 24. ISSN 2073-4336
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Rock-Paper-Scissors; Cyclic Dominance; Pattern Formation; Spiral Waves; Diffusion; Phase Diagram; Individual-Based Modelling; Stochastic Lattice Simulations; Complex Ginzburg-Landau Equation |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 02 Sep 2016 12:41 |
Last Modified: | 23 Jun 2023 22:12 |
Published Version: | http://dx.doi.org/10.3390/g7030024 |
Status: | Published |
Publisher: | MDPI |
Identification Number: | 10.3390/g7030024 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:104265 |