Cyclic competition of mobile species on continuous space: pattern formation and coexistence

Xuan Ni, Wen-Xu Wang, Ying-Cheng Lai, Celso Grebogi

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)


We propose a model for cyclically competing species on continuous space and investigate the effect of the interplay between the interaction range and mobility on coexistence. A transition from coexistence to extinction is uncovered with a strikingly nonmonotonic behavior in the coexistence probability. About the minimum in the probability, switches between spiral and plane-wave patterns arise. A strong mobility can either promote or hamper coexistence, depending on the radius of the interaction range. These phenomena are absent in any lattice-based model, and we demonstrate that they can be explained using nonlinear partial differential equations. Our continuous-space model is more physical and we expect the findings to generate experimental interest.

Original languageEnglish
Article number066211
Number of pages8
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number6
Publication statusPublished - 23 Dec 2010


  • rock-paper-scissors
  • promotes biodiversity
  • spiral waves
  • populations
  • game
  • hypercycles
  • dynamics
  • chaos
  • allelopathy
  • evolution


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