Spatio-temporal chaos for the Gray-Scott model

Yasumasa Nishiura, Daishin Ueyama

Research output: Contribution to journalArticlepeer-review

115 Citations (Scopus)


A new geometrical criterion for the transition to spatio-temporal chaos (STC) arising in the Gray-Scott model is presented. This is based on the inter-relationship of global bifurcating branches of ordered patterns with respect to supply and removal rates contained in the model. This viewpoint not only gives us a new criterion for the onset of STC but also clarifies how the orbit itinerates among several ordered patterns in infinite-dimensional space. Moreover, the geometrical characterization gives us a universal viewpoint about the onset and termination of STC. There are at least two different mechanisms that cause re-injection dynamics and drive the STC: one is a generalized heteroclinic cycle consisting of self-replication and self-destruction processes, and the other involves annihilation of colliding waves instead of self-destruction.

Original languageEnglish
Pages (from-to)137-162
Number of pages26
JournalPhysica D: Nonlinear Phenomena
Issue number3-4
Publication statusPublished - 2001 Apr 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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