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Coexistence in a one-dimensional cyclic dominance process

Anton A. Winkler, Tobias Reichenbach, and Erwin Frey
Phys. Rev. E 81, 060901(R) – Published 28 June 2010
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Abstract

Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and nonequilibrium processes in the stationary state. We exploit these insights to obtain asymptotically exact descriptions of the emerging reactive steady state in the regimes of high and low mutation rates. The results are compared to stochastic lattice simulations. Our methods and findings are potentially relevant for the spatiotemporal evolution of other nonequilibrium stochastic processes.

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  • Received 27 November 2009

DOI:https://doi.org/10.1103/PhysRevE.81.060901

©2010 American Physical Society

Authors & Affiliations

Anton A. Winkler1, Tobias Reichenbach2, and Erwin Frey1

  • 1Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333 München, Germany
  • 2Howard Hughes Medical Institute and Laboratory of Sensory Neuroscience, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA

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Issue

Vol. 81, Iss. 6 — June 2010

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