Defensive alliances in spatial models of cyclical population interactions

György Szabó, T. Czárán

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume64
Issue number4
DOIs
Publication statusPublished - Jan 1 2001

Fingerprint

Spatial Model
mutations
sociology
organizing
games
Mutation
biology
Interaction
economics
Dynamic Games
topology
Invasion
interactions
rocks
Self-organizing
Square Lattice
Ising
Biology
Isomorphic
Economics

ASJC Scopus subject areas

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

Cite this

@article{f124ff49b8cf4cce8589e509c77c7558,
title = "Defensive alliances in spatial models of cyclical population interactions",
abstract = "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.",
author = "Gy{\"o}rgy Szab{\'o} and T. Cz{\'a}r{\'a}n",
year = "2001",
month = "1",
day = "1",
doi = "10.1103/PhysRevE.64.042902",
language = "English",
volume = "64",
journal = "Physical review. E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "4",

}

TY - JOUR

T1 - Defensive alliances in spatial models of cyclical population interactions

AU - Szabó, György

AU - Czárán, T.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84884168454&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884168454&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.64.042902

DO - 10.1103/PhysRevE.64.042902

M3 - Article

AN - SCOPUS:84884168454

VL - 64

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 4

ER -