Three- and four-state rock-paper-scissors games with diffusion

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© 2008 American Physical Society (APS). This is the accepted version of the following article: Peltomäki, Matti & Alava, Mikko J. 2008. Three- and four-state rock-paper-scissors games with diffusion. Physical Review E. Volume 78, Issue 3. 031906/1-7. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.78.031906, which has been published in final form at http://journals.aps.org/pre/abstract/10.1103/PhysRevE.78.031906.
Journal Title
Journal ISSN
Volume Title
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2008
Major/Subject
Mcode
Degree programme
Language
en
Pages
031906/1-7
Series
Physical Review E, Volume 78, Issue 3
Abstract
Cyclic dominance of three species is a commonly occurring interaction dynamics, often denoted the rock-paper-scissors (RPS) game. Such a type of interactions is known to promote species coexistence. Here, we generalize recent results of Reichenbach et al. [Nature (London) 448, 1046 (2007)] of a four-state variant of the RPS game. We show that spiral formation takes place only without a conservation law for the total density. Nevertheless, in general, fast diffusion can destroy species coexistence. We also generalize the four-state model to slightly varying reaction rates. This is shown both analytically and numerically not to change pattern formation, or the effective wavelength of the spirals, and therefore not to alter the qualitative properties of the crossover to extinction.
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Keywords
cyclic dominance of three species, rock-paper-scissors games
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Citation
Peltomäki, Matti & Alava, Mikko J. 2008. Three- and four-state rock-paper-scissors games with diffusion. Physical Review E. Volume 78, Issue 3. 031906/1-7. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.78.031906.