Pattern formation in non-gradient reaction-diffusion systems: The effects of front bifurcations

A. Hagberg, E. Meron

Research output: Contribution to journalArticlepeer-review

187 Scopus citations


Domain patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally develop in bistable and excitable systems, but may also appear far beyond Hopf and Turing bifurcations. The global behaviour of domain patterns strongly depends on the fronts' inner structures. In this paper we study a symmetry breaking front bifurcation expected to occur in a wide class of reaction-diffusion systems, and the effects it has on pattern formation and pattern dynamics. We extend previous works on this type of front bifurcation and clarify the relations among them. We show that the appearance of front multiplicity beyond the bifurcation point allows the formation of persistent patterns rather than transient ones. In a different parameter regime, we find that the front bifurcation outlines a transition from oscillating (or breathing) patterns to travelling ones. Near a boundary we find that fronts beyond the bifurcation can reflect, while those below it either bind to the boundary or disappear.

Original languageEnglish
Article number006
Pages (from-to)805-835
Number of pages31
Issue number3
StatePublished - 1 Dec 1994

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy (all)
  • Applied Mathematics


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