Defensive alliances in spatial models of cyclical population interactions

Details Defensive alliances in spatial models of cyclical population interactions Defensive alliances in spatial models of cyclical population interactions

2001-03-30

arxiv.org/abs/cond-mat/0103625v1

Phys. Rev. E, 64 (2001) 042902.

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevE.64.042902

As a generalization of the 3-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, these systems can be classified into four (isomorphic) groups exhibiting significantly different behaviors as a function of mutation rate. On three out of four cases three (or four) species form defensive alliances which 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 model.

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