Spatial patterns for an interaction-diffusion equation in morphogenesis

Masayasu Mimura, Yasumasa Nishiura

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

A certain interaction-diffusion equation occurring in morphogenesis is considered. This equation is proposed by Gierer and Meinhardt, which is introduced by Child's gradient theory and Turing's idea about diffusion driven instability. It is shown that slightly asymmetric gradients in the tissue produce stable striking patterns depending on its asymmetry, starting from uniform distribution of morphogens. The tool is the perturbed bifurcation theory. Moreover, from a mathematical point of view, the global existence of steady state solutions with respect to some parameters is discussed.

Original languageEnglish
Pages (from-to)243-263
Number of pages21
JournalJournal of Mathematical Biology
Volume7
Issue number3
DOIs
Publication statusPublished - 1979 Apr
Externally publishedYes

Keywords

  • Bifurcation
  • Morphogenesis
  • Non-linear diffusion
  • Spatial patterns

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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