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 language | English |
|---|---|
| Number of pages | 1 |
| Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
| Volume | 64 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Jan 1 2001 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics
Cite this
Defensive alliances in spatial models of cyclical population interactions. / Szabó, György; Czárán, T.
In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 64, No. 4, 01.01.2001.Research output: Contribution to journal › Article
}
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.
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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 -