Defensive alliances in spatial models of cyclical population interactions

György Szabó, Tamás Czárán

Research output: Contribution to journalArticle

2 Citations (Scopus)


As a generalization of the three-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated, and a neutral interacting partner. Depending on their interaction topologies, all imaginable systems can be classified into four (isomorphic) groups exhibiting significantly different behaviors as a function of mutation rate. In three out of four cases three (or four) species form defensive alliances that maintain themselves in a self-organizing polydomain structure via cyclic invasions. Varying the mutation rate, this mechanism results in an ordering phenomenon analogous to that of magnetic Ising systems. The model explains a very basic mechanism of community organization, which might gain important applications in biology, economics, and sociology.

Original languageEnglish
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number4
Publication statusPublished - Jan 1 2001

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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