Szczesny, B, Mobilia, M and Rucklidge, AM (2014) Characterization of spiraling patterns in spatial rock-paper-scissors games. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 90 (3). 032704. ISSN 1539-3755
Abstract
The spatiotemporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatiotemporal patterns arising from the cyclic competition between three species in two dimensions. Inspired by recent experiments, we consider a generic metapopulation model comprising “rock-paper-scissors” interactions via dominance removal and replacement, reproduction, mutations, pair exchange, and hopping of individuals. By combining analytical and numerical methods, we obtain the model's phase diagram near its Hopf bifurcation and quantitatively characterize the properties of the spiraling patterns arising in each phase. The phases characterizing the cyclic competition away from the Hopf bifurcation (at low mutation rate) are also investigated. Our analytical approach relies on the careful analysis of the properties of the complex Ginzburg-Landau equation derived through a controlled (perturbative) multiscale expansion around the model's Hopf bifurcation. Our results allow us to clarify when spatial “rock-paper-scissors” competition leads to stable spiral waves and under which circumstances they are influenced by nonlinear mobility.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | ©2014 American Physical Society. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | q-bio.PE; q-bio.PE; cond-mat.stat-mech; nlin.PS; q-bio.QM |
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 Jul 2015 15:07 |
Last Modified: | 04 Feb 2018 06:55 |
Published Version: | http://dx.doi.org/10.1103/PhysRevE.90.032704 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevE.90.032704 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:84733 |