Phase transition and selection in a four-species cyclic predator-prey model

G. Szabó, Gustavo Arial Sznaider

Research output: Contribution to journalArticle

71 Citations (Scopus)

Abstract

We study a four-species ecological system with cyclic dominance whose individuals are distributed on a square lattice. Randomly chosen individuals migrate to one of the neighboring sites if it is empty or invade this site if occupied by their prey. The cyclic dominance maintains the coexistence of all four species if the concentration of vacant sites is lower than a threshold value. Above the threshold, a symmetry breaking ordering occurs via growing domains containing only two neutral species inside. These two neutral species can protect each other from the external invaders (predators) and extend their common territory. According to our Monte Carlo simulations the observed phase transition seems to be equivalent to those found in spreading models with two equivalent absorbing states although the present model has continuous sets of absorbing states with different portions of the two neutral species. The selection mechanism yielding symmetric phases is related to the domain growth process with wide boundaries where the four species coexist.

Original languageEnglish
Pages (from-to)31911
Number of pages1
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume69
Issue number3
Publication statusPublished - Mar 1 2004

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predators
Phase Transition
Predator-prey Model
Ecosystem
thresholds
ecosystems
Growth
broken symmetry
Absorbing
Domain Growth
simulation
Growth Process
Predator
Prey
Threshold Value
Square Lattice
Coexistence
Symmetry Breaking
Monte Carlo Simulation
Model

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Cite this

Phase transition and selection in a four-species cyclic predator-prey model. / Szabó, G.; Arial Sznaider, Gustavo.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 69, No. 3, 01.03.2004, p. 31911.

Research output: Contribution to journalArticle

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