Bulletin of Mathematical Biology

, Volume 75, Issue 12, pp 2346–2371 | Cite as

Reaction-Diffusion Patterns in Plant Tip Morphogenesis: Bifurcations on Spherical Caps

  • Wayne NagataEmail author
  • Hamid R. Z. Zangeneh
  • David M. Holloway
Original Article


We study a chemical reaction-diffusion model (the Brusselator) for pattern formation on developing plant tips. A family of spherical cap domains is used to represent tip flattening during development. Applied to conifer embryos, we model the chemical prepatterning underlying cotyledon (“seed leaf”) formation, and demonstrate the dependence of patterns on tip flatness, radius, and precursor concentrations. Parameters for the Brusselator in spherical cap domains can be chosen to give supercritical pitchfork bifurcations of patterned solutions of the nonlinear reaction-diffusion system that correspond to the cotyledon patterns that appear on the flattening tips of conifer embryos.


Reaction-diffusion patterns Plant development 



We thank NSERC (Canada), Isfahan University of Technology and British Columbia Institute of Technology for financial support, T.C. Lacalli for stimulating discussions, and P. von Aderkas for the images in Fig. 1.


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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  • Wayne Nagata
    • 1
    Email author
  • Hamid R. Z. Zangeneh
    • 2
  • David M. Holloway
    • 3
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran
  3. 3.Mathematics DepartmentBritish Columbia Institute of TechnologyBurnabyCanada

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