Three- and four-state rock-paper-scissors games with diffusion.
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 [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.
Department of Engineering Physics, Helsinki University of Technology, P.O. Box 1100, 02015 HUT, Espoo, Finland.
Matti
M
Peltomäki
Mikko
M
Alava
D000465:Algorithms; D000818:Animals; D044822:Biodiversity; D003198:Computer Simulation; D004058:Diffusion; D004463:Ecology; D017753:Ecosystem; D005716:Game Theory; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D011157:Population Dynamics; D011336:Probability; D013997:Time Factors