Apparition de motifs géométriques dans une membrane enzymatique

 Access to full text

 Full (PDF)

1. [1] A. M. TURING, The chemical basis of morphogenesis, Phil. Trans. Roy. Soc. London,Vol. B 237 (1952), 37-72. 
2. [2] I. PRJGOGINE et G. NICOLIS, On symmetry breaking instabilities in dissipativeSystems, J. Chem. Phys., 46 (1967), 3542-3550. 
3. [3] I. PRIGOGINE, R. LEFEVER, A. GOLDBETER et M. HERSCHKOWITZ-KAUFMAN, Symmetry breaking instabilities in biological Systems, Nature, 223 (1969), 913-916. 
4. [4] H. G. OTHMER et L. E. SCRTVEN, Instability and dynamic pattern in cellular networks, J. Theor. Biol., 32 (1971), 507-537. 
5. [5] A. GIERER et H. MEINHARDT, A theory of biological pattern formation, Kybernetika (Prague) 12 (1972), 30-39. Zbl0297.92007
6. [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. [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. Zbl0317.92016
8. [8] B.C. GOODWIN, Analytical physiology of cells and deveioping organisms (Academic Press, New York, 1976). 
9. [9] J. D. MURRAY, Lectures on nonlinear differential-equation models in biology Clarendon Press, Oxford, 1977). Zbl0379.92001
10. [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). Zbl0363.93005MR522141
11. [11] M. MIMURA et J. D. MURRAY, Spatial structures in a model substrate-inhibitiondiffusion System, Z.Naturforsch, 33 C (1978), 580-586. 
12. [12] P. C. FIFE, Mathematical aspects of reacting and diffusing Systems, (Springer-Verlag, Berlin, 1979). Zbl0403.92004MR527914
13. [13] J. HIERNAUX et T. ERNEUX, Chemical patterns in circular morphogenetic fields, Bull. Math. Biol., 41 (1979), 461-468. MR631874
14. [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. Zbl0433.92014MR648839
15. [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. [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. [17] A. GARCIA-BELLIDO, P. RIPOLL et P. MORATA, Developmental compartmentaliza-tion ofthe wing disk of Drosophila, Nature NewBiol., 245(1973), 251-253. 
18. [18] J. P. KERNEVEZ, Enzyme Mathematics : Studies in Mathematics and its applications, Vol. 10 (North-Holland, 1980). Zbl0446.92007MR594596
19. [19] G. MEURAUT et J. C. SAUT, Bifurcation and stability in a chemical system, J. Math. Anal, and Appi. 59 (1977), 69-91. Zbl0355.35009MR462242
20. [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. Zbl0328.76065
21. [21] D. HENRY, Geometrie theory of semilinear parabolie équations, lecture notes in Vlathematics n° 840, Springer-Verlag, NewYork, 1981. Zbl0456.35001MR610244
22. [22] KATO T., Perturbation theory for linear operators (Springer-Verlag, New York, 1960). Zbl0435.47001
23. [23] G. LOSS, Bifurcation et stabilité. Publications mathématiques d'Orsay, N° 31 (Université de Paris Sud, Orsay, 1972). 
24. [24] H.P. KEENER et H. B. KELLER, Perturbed bifurcation theory, Arch. Rat. Mech. Anal., Vol. 50 (1973), 159-175. Zbl0254.47080MR336479
25. [25] D. W. DECKER, Topics in bifurcation theory, Ph. D. Thesis, California ïnstitute of Technology, Pasadena, California, 1978. 
26. [26] H. B. KELLER, TWOnewbifurcation phenomena, IRIA Research Report n° 369 (1979). Zbl0505.35009
27. [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. Zbl0275.47044MR341212
28. [28] M. KUBICEK, Dependence of solution of nonlinear Systems on a parameter, ACM Transactions on Mathematical Software, Vol 2, 1 (March 1976), 98-107. Zbl0317.65019
29. [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). Zbl0581.65043MR455353
30. [30] G. JOLY, J. P. KERNEVEZ, M. SHARAN, Calculation of the bifurcation branches inreaction-difjusion Systems (à paraître dans Acta Applicandae Mathematicae). 
31. [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. Zbl0523.92008
32. [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. Zbl0391.65050MR520780
33. [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. Zbl0499.65041MR784656