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Turing's theory in morphogenesis

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Abstract

Bifurcation theoretical and numerical analyses of one of Turing's models are performed. It is shown that at the first instability point of the homogeneous state the bifurcating branches aresubcritical, and thus emerge as unstable solutions. This, together with the presence of concentration-independent sink terms is responsible for the solutions becoming negative ast→∞. It is pointed out that this deficiency is an accident related to the choice of the model, and that the general idea of symmetry-breaking is perfectly compatible with the generation of regular morphogenetic patterns.

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Authors and Affiliations

  1. Faculté des Sciences de l'Université Libre de Bruxelles, Campus Plaine, B.P. 231, 1050, Bruxelles, Belgium

    T. Erneux, J. Hiernaux & G. Nicolis

Authors
  1. T. Erneux
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  2. J. Hiernaux
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  3. G. Nicolis
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Erneux, T., Hiernaux, J. & Nicolis, G. Turing's theory in morphogenesis. Bltn Mathcal Biology 40, 771–789 (1978). https://doi.org/10.1007/BF02460606

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  • DOI: https://doi.org/10.1007/BF02460606

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