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Pattern formation and wave propagation in the s-a system

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Bifurcation and Nonlinear Eigenvalue Problems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 782))

Abstract

A system of two coupled reaction-diffusion equations involving substrate inhibited enzyme kinetics is studied with a view to describing and explaining stable non uniform steady state solutions and propagating wave front solutions which they admit. The pattern formation phenomenon, reminiscent of morphogenesis, is compared to the predictions of Kauffman for sequential compartment formation in Drosophila imaginal disks. A modified perturbation technique is used to obtain the emerging bifurcation branches.

Numerical analysis of pattern formation needs methods to follow branches of solutions including turning points and bifurcation points. A simple dissipative structure is given in order to test such algorithms.

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Authors and Affiliations

  1. Université de Technologie de Compiègne, B.P. 233, 60206, Compiègne, France

    J. P. Kernevez, G. Joly & D. Thomas

  2. National Institute of Health, 20014, Bethesda, Maryland, U.S.A.

    B. Bunow

Authors
  1. J. P. Kernevez
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  2. G. Joly
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  3. D. Thomas
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  4. B. Bunow
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Editor information

C. Bardos J. M. Lasry M. Schatzman

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© 1980 Springer-Verlag

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Kernevez, J.P., Joly, G., Thomas, D., Bunow, B. (1980). Pattern formation and wave propagation in the s-a system. In: Bardos, C., Lasry, J.M., Schatzman, M. (eds) Bifurcation and Nonlinear Eigenvalue Problems. Lecture Notes in Mathematics, vol 782. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090434

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  • DOI: https://doi.org/10.1007/BFb0090434

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  • Print ISBN: 978-3-540-09758-7

  • Online ISBN: 978-3-540-38637-7

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