A mechanical model for biological pattern formation: A nonlinear bifurcation analysis

  • P. K. Maini
  • J. D. Murray
  • G. F. Oster
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1151)


We present a mechanical model for cell aggregation in embryonic development. The model is based on the large traction forces exerted by fibroblast cells which deform the extracellular matrix (ECM) on which they move. It is shown that the subsequent changes in the cell environment can combine to produce pattern. A linear analysis is carried out for this model. This reveals a wide spectrum of different types of dispersion relations. A non-linear bifurcation analysis is presented for a simple version of the field equations: a non-standard element is required. Biological applications are briefly discussed.


Dispersion Relation Homogeneous Steady State Uniform Steady State Biological Pattern Formation Chick Wing 
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© Springer-Verlag 1985

Authors and Affiliations

  • P. K. Maini
  • J. D. Murray
  • G. F. Oster

There are no affiliations available

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