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

Matti Peltomäki, M. Alava

Research output: Contribution to journalArticleScientificpeer-review

90 Citations (Scopus)
5 Downloads (Pure)


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.
Original languageEnglish
Article number031906
Pages (from-to)1-7
JournalPhysical Review E
Issue number3
Publication statusPublished - 2008
MoE publication typeA1 Journal article-refereed


  • diffusion


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