Berlin 2008 – scientific programme
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SYDN: Symposium Game theory in dynamical systems
SYDN 1: Game theory in dynamical systems
SYDN 1.7: Talk
Friday, February 29, 2008, 12:05–12:20, H 0105
Mobility and pattern formation in rock-paper-scissors games — •Tobias Reichenbach1, Mauro Mobilia2, and Erwin Frey1 — 1Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany — 2Mathematics Institute and Warwick Complexity Complex, The University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
Self-formation of noisy patterns governs species coevolution in spatially extended, biodiverse ecosystems. Individuals that organize into such patterns are often mobile: bacteria run and tumble, and animals migrate from place to place. We show that mobility has intriguing impact on form and size of the self-forming spatial structures, and thereby on the possibility of species diversity. Employing a specific model for cyclic (rock-paper-scissors-type) competition of species, we show that, under the influence of mobility, surprisingly regular, geometric patterns form. Namely, a noisy entanglement of rotating spiral waves self-organizes in the course of time. A critical value of mobility separates this biodiverse scenario from a uniform one where only one species survives.
[1] Tobias Reichenbach, Mauro Mobilia, Erwin Frey, Nature 448, 1046-1049 (2007)
[2] Tobias Reichenbach, Mauro Mobilia, Erwin Frey, Phys. Rev. Lett. in print (2007)