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Bulletin of Mathematical Biology

, Volume 68, Issue 5, pp 981–995 | Cite as

Mode Transitions in a Model Reaction–Diffusion System Driven by Domain Growth and Noise

  • Iain Barrass
  • Edmund J. Crampin
  • Philip K. Maini
Original Paper

Abstract

Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns.

Keywords

Turing model Schnakenberg Spatial pattern Robustness Mode-doubling failure Mode selection 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Iain Barrass
    • 1
  • Edmund J. Crampin
    • 1
    • 2
  • Philip K. Maini
    • 1
  1. 1.Centre for Mathematical Biology, Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.Bioengineering Institute and Department of Engineering ScienceThe University of AucklandAucklandNew Zealand

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