Turbulence in diffusion replicator equation

Kenji Orihashi*, Yoji Aizawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Dynamical behaviors in the diffusion replicator equation of three species are numerically studied. We point out the significant role of the heteroclinic cycle in the equation, and analyze the details of the turbulent solution that appeared in this system. Firstly, the bifurcation diagram for a certain parameter setting is drawn. Then it is shown that the turbulence appears with the supercritical Hopf bifurcation of a stationary uniform solution and it disappears under a subcritical-type bifurcation. Secondly, the statistical property of the turbulence near the supercritical Hopf onset point is analyzed precisely. Further, the correlation lengths and correlation times obey some characteristic scaling laws.

Original languageEnglish
Pages (from-to)3053-3060
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Issue number23
Publication statusPublished - 2008 Dec 1


  • Correlation length and time
  • Diffusion replicator equation
  • Scaling law
  • Spatio-temporal chaos

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics


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