Diverging fluctuations in a spatial five-species cyclic dominance game

Vukov, Jeromos and Szolnoki, Attila and Szabó, György (2013) Diverging fluctuations in a spatial five-species cyclic dominance game. PHYSICAL REVIEW E - STATISTICAL, NONLINEAR AND SOFT MATTER PHYSICS, 88 (2). ISSN 1539-3755

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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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