Diverging fluctuations in a spatial five-species cyclic dominance game

Jeromos Vukov, Attila Szolnoki, and György Szabó
Phys. Rev. E 88, 022123 – Published 14 August 2013

Abstract

A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the rock-paper-scissors-lizard-Spock game. The evolution of the spatial distribution of species is governed by site exchange and invasion between the neighboring predator-prey pairs, where the cyclic symmetry can be characterized by two different invasion rates. The mean-field analysis has indicated periodic oscillations in the species densities with a frequency becoming zero for a specific ratio of invasion rates. When varying the ratio of invasion rates, the appearance of this zero-eigenvalue mode is accompanied by neutrality between the species associations. Monte Carlo simulations of the spatial system reveal diverging fluctuations at a specific invasion rate, which can be related to the vanishing dominance between all pairs of species associations.

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  • Received 6 June 2013

DOI:https://doi.org/10.1103/PhysRevE.88.022123

©2013 American Physical Society

Authors & Affiliations

Jeromos Vukov1,*, Attila Szolnoki1, and György Szabó1,2

  • 1Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
  • 2Roland Eötvös University, Regional Knowledge Centre, Irányi Dániel u. 4, H-8000 Székesfehérvár, Hungary

  • *vukov@mfa.kfki.hu

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Vol. 88, Iss. 2 — August 2013

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