Basins of attraction for species extinction and coexistence in spatial rock-paper-scissors games

Hongjing Shi, Wen Xu Wang, Rui Yang, Ying-Cheng Lai

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

We study the collective dynamics of mobile species under cyclic competition by breaking the symmetry in the initial populations and examining the basins of the two distinct asymptotic states: extinction and coexistence, the latter maintaining biodiversity. We find a rich dependence of dynamical properties on initial conditions. In particular, for high mobility, only extinction basins exist and they are spirally entangled, but a basin of coexistence emerges when the mobility parameter is decreased through a critical value, whose area increases monotonically as the parameter is further decreased. The structure of extinction basins for high mobility can be predicted by a mean-field theory. These results provide a more comprehensive picture for the fundamental issue of species coexistence than previously achieved.

Original languageEnglish (US)
Article number030901
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume81
Issue number3
DOIs
StatePublished - Mar 1 2010

Fingerprint

Basin of Attraction
games
Coexistence
Extinction
attraction
extinction
rocks
Game
Biodiversity
Mean-field Theory
biological diversity
Critical value
Initial conditions
Distinct
Symmetry
symmetry

ASJC Scopus subject areas

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

Cite this

Basins of attraction for species extinction and coexistence in spatial rock-paper-scissors games. / Shi, Hongjing; Wang, Wen Xu; Yang, Rui; Lai, Ying-Cheng.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 81, No. 3, 030901, 01.03.2010.

Research output: Contribution to journalArticle

@article{f62b50d83a7c43aa84e4d1406ba793b7,
title = "Basins of attraction for species extinction and coexistence in spatial rock-paper-scissors games",
abstract = "We study the collective dynamics of mobile species under cyclic competition by breaking the symmetry in the initial populations and examining the basins of the two distinct asymptotic states: extinction and coexistence, the latter maintaining biodiversity. We find a rich dependence of dynamical properties on initial conditions. In particular, for high mobility, only extinction basins exist and they are spirally entangled, but a basin of coexistence emerges when the mobility parameter is decreased through a critical value, whose area increases monotonically as the parameter is further decreased. The structure of extinction basins for high mobility can be predicted by a mean-field theory. These results provide a more comprehensive picture for the fundamental issue of species coexistence than previously achieved.",
author = "Hongjing Shi and Wang, {Wen Xu} and Rui Yang and Ying-Cheng Lai",
year = "2010",
month = "3",
day = "1",
doi = "10.1103/PhysRevE.81.030901",
language = "English (US)",
volume = "81",
journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
issn = "1539-3755",
publisher = "American Physical Society",
number = "3",

}

TY - JOUR

T1 - Basins of attraction for species extinction and coexistence in spatial rock-paper-scissors games

AU - Shi, Hongjing

AU - Wang, Wen Xu

AU - Yang, Rui

AU - Lai, Ying-Cheng

PY - 2010/3/1

Y1 - 2010/3/1

N2 - We study the collective dynamics of mobile species under cyclic competition by breaking the symmetry in the initial populations and examining the basins of the two distinct asymptotic states: extinction and coexistence, the latter maintaining biodiversity. We find a rich dependence of dynamical properties on initial conditions. In particular, for high mobility, only extinction basins exist and they are spirally entangled, but a basin of coexistence emerges when the mobility parameter is decreased through a critical value, whose area increases monotonically as the parameter is further decreased. The structure of extinction basins for high mobility can be predicted by a mean-field theory. These results provide a more comprehensive picture for the fundamental issue of species coexistence than previously achieved.

AB - We study the collective dynamics of mobile species under cyclic competition by breaking the symmetry in the initial populations and examining the basins of the two distinct asymptotic states: extinction and coexistence, the latter maintaining biodiversity. We find a rich dependence of dynamical properties on initial conditions. In particular, for high mobility, only extinction basins exist and they are spirally entangled, but a basin of coexistence emerges when the mobility parameter is decreased through a critical value, whose area increases monotonically as the parameter is further decreased. The structure of extinction basins for high mobility can be predicted by a mean-field theory. These results provide a more comprehensive picture for the fundamental issue of species coexistence than previously achieved.

UR - http://www.scopus.com/inward/record.url?scp=77749280123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77749280123&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.81.030901

DO - 10.1103/PhysRevE.81.030901

M3 - Article

C2 - 20365687

AN - SCOPUS:77749280123

VL - 81

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 3

M1 - 030901

ER -