Free Access
Issue
RAIRO. Anal. numér.
Volume 18, Number 1, 1984
Page(s) 87 - 116
DOI https://doi.org/10.1051/m2an/1984180100871
Published online 31 January 2017
  1. A. M. TURING, The chemical basis of morphogenesis, Phil. Trans. Roy. Soc. London,Vol. B 237 (1952), 37-72.
  2. I. PRJGOGINE et G. NICOLIS, On symmetry breaking instabilities in dissipativeSystems, J. Chem. Phys., 46 (1967), 3542-3550.
  3. I. PRIGOGINE,R. LEFEVER, A. GOLDBETER et M. HERSCHKOWITZ-KAUFMAN, Symmetry breaking instabilities in biological Systems, Nature, 223 (1969), 913-916.
  4. H. G. OTHMER et L. E. SCRTVEN, Instability and dynamic pattern in cellular networks, J. Theor. Biol., 32 (1971), 507-537.
  5. A. GIERER et H. MEINHARDT, A theory of biological pattern formation, Kybernetika (Prague) 12 (1972), 30-39. [Zbl: 0297.92007]
  6. L. WOLPERT, Positional information and the developmenl of pattern and form: Cowan J. D. (éd.), Some mathematical questions in biology 5 (The American Mathematical Society, Providence, 1974).
  7. A. BABLOYANTZ et J. HIERNAUX, Modeis for cell differentiation and génération ofpolarity in diffusion-controlled morphogenetic fields, Bull. Math. Biol., 37 (1975), 637-657. [Zbl: 0317.92016]
  8. B.C. GOODWIN, Analytical physiology of cells and deveioping organisms (Academic Press, New York, 1976).
  9. J. D. MURRAY, Lectures on nonlinear differential-equation models in biology Clarendon Press, Oxford, 1977). [Zbl: 0379.92001]
  10. G. NICOLIS et I. PRIGOGINE, Self-organization in nonequilibrium Systems, frontdissipative structures to order through fluctuations, fronmdissipative structures to order through fluctuations (Wiley-Interscience, New York, 1977). [MR: 522141] [Zbl: 0363.93005]
  11. M. MIMURA et J. D. MURRAY, Spatial structures in a model substrate-inhibitiondiffusion System, Z.Naturforsch, 33 C (1978), 580-586.
  12. P. C. FIFE, Mathematical aspects of reacting and diffusing Systems, (Springer-Verlag, Berlin, 1979). [MR: 527914] [Zbl: 0403.92004]
  13. J. HIERNAUX et T. ERNEUX, Chemical patterns in circular morphogenetic fields, Bull. Math. Biol., 41 (1979), 461-468. [MR: 631874]
  14. J. P. KERNEVEZ,G. JOLY, M. C. DUBAN , B. BUNOW and D. THOMAS, Hystérésis,oscillations andpattern formation inrealistic immobilized enzyme Systems,J. Math. Biology, 7 (1979), 41-56. [MR: 648839] [Zbl: 0433.92014]
  15. S. A. KAUFFMAN,R. M. SHYMKO et K. TRABERT, Control of sequential compartmentformation in Drosophila, a uniform mechanism may control the locations of successivebinary developmental commitments, Science, Vol. 199 (1978), 259-270.
  16. A. GARCIA-BELLIDO et J. P. MERRIAM, Parameters of the wing imaginal disc deve-lopment of Drosophila melanogaster, Develop. Biol., 24 (1971), 61-87.
  17. A. GARCIA-BELLIDO,P. RIPOLL et P. MORATA, Developmental compartmentaliza-tion ofthe wing disk of Drosophila, Nature NewBiol., 245(1973), 251-253.
  18. J. P. KERNEVEZ, Enzyme Mathematics : Studies in Mathematics and its applications, Vol. 10 (North-Holland, 1980). [MR: 594596] [Zbl: 0446.92007]
  19. G. MEURAUT et J. C. SAUT, Bifurcation and stability in a chemical system, J. Math. Anal, and Appi. 59 (1977), 69-91. [MR: 462242] [Zbl: 0355.35009]
  20. J. A. BOA et D. S. COHEN, Bifurcation of localized disturbances in a model bioche-mical reaction, Siam J. Appl. Math., Vol. 30, n° 1(1976), 123-135. [Zbl: 0328.76065]
  21. D. HENRY, Geometrie theory of semilinear parabolie équations, lecture notes in Vlathematics n° 840, Springer-Verlag, NewYork, 1981. [MR: 610244] [Zbl: 0456.35001]
  22. KATO T., Perturbation theory for linear operators (Springer-Verlag, New York, 1960). [Zbl: 0435.47001]
  23. G. LOSS, Bifurcation et stabilité. Publications mathématiques d'Orsay, N° 31 (Université de Paris Sud, Orsay, 1972).
  24. H.P. KEENER et H. B. KELLER, Perturbed bifurcation theory, Arch. Rat. Mech. Anal., Vol. 50 (1973), 159-175. [MR: 336479] [Zbl: 0254.47080]
  25. D. W. DECKER, Topics in bifurcation theory, Ph. D. Thesis, California ïnstitute of Technology, Pasadena, California, 1978.
  26. H. B. KELLER, TWOnewbifurcation phenomena, IRIA Research Report n° 369 (1979). [Zbl: 0505.35009]
  27. M. G. CRANDALL et P. H. RABINOWITZ, Bifurcation, perturbation of simple eigen values, and linearized stability, Arch. Rat. Mech. Anal. 52 (1973), 161-180. [MR: 341212] [Zbl: 0275.47044]
  28. M. KUBICEK, Dependence of solution of nonlinear Systems on a parameter, ACM Transactions on Mathematical Software, Vol 2, 1 (March 1976), 98-107. [Zbl: 0317.65019]
  29. H.B. KELLER, Numerical solution of bifurcation andnon linear eigen value problems, 359-384 : Rabinowitz P.H. (éd.), Applications of bifurcation theory (Academic Press, New York, 1977). [MR: 455353] [Zbl: 0581.65043]
  30. G. JOLY, J. P. KERNEVEZ, M. SHARAN, Calculation of the bifurcation branches inreaction-difjusion Systems (à paraître dans Acta Applicandae Mathematicae).
  31. J. P. KERNEVEZ,E. DOEDEL, M. C. DUBAN, J. F. HERVAGAULT, G. JOLY et D. THOMAS, Spatio-temporal organization in immobilized enzyme Systems, à paraître. [Zbl: 0523.92008]
  32. J. P. KERNEVEZ,J. D. MURRAY, G. JOLY, M. C. DUBAN et D. THOMAS, Propagationd'onde dans un système à enzyme immobilisée, CRAS 387, A (1978), 961-964. [MR: 520780] [Zbl: 0391.65050]
  33. J. P. KERNEVEZ,G. JOLY et M. SHARAN, Control of Systems with multiple steadystates, pp. 635-649 in : Glowinski, R. and Lions, J. L. (éd.), Computing Methods in Applied Sciences and Engineering, North Holland, Amsterdam, 1982. [MR: 784656] [Zbl: 0499.65041]

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