Front motion and localized states in an asymmetric bistable activator-inhibitor system with saturation

Arik Yochelis, Alan Garfinkel

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We study the spatiotemporal properties of coherent states (peaks, holes, and fronts) in a bistable activator-inhibitor system that exhibits biochemical saturated autocatalysis, and in which fronts do not preserve spatial parity symmetry. Using the Gierer-Meinhardt prototype model, we find the conditions in which two distinct pinning regions are formed. The first pinning type is known in the context of variational systems while the second is structurally different due to the presence of a heteroclinic bifurcation between two uniform states. The bifurcation also separates the parameter regions of counterpropagating fronts, leading in turn to the growth or contraction of activator domains. These phenomena expand the range of pattern formation theory and its biomedical applications: activator domain retraction suggests potential therapeutic strategies for patterned pathologies, such as cardiovascular calcification.

Original languageEnglish
Article number035204
JournalPhysical Review E
Volume77
Issue number3
DOIs
StatePublished - 20 Mar 2008
Externally publishedYes

ASJC Scopus subject areas

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

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