Apparition de motifs géométriques dans une membrane enzymatique
RAIRO. Analyse numérique, Tome 18 (1984) no. 1, pp. 87-116. 
@article{M2AN_1984__18_1_87_0,
     author = {Joly, G. and Kernevez, J. P.},
     title = {Apparition de motifs g\'eom\'etriques dans une membrane enzymatique},
     journal = {RAIRO. Analyse num\'erique},
     pages = {87--116},
     publisher = {Centrale des revues, Dunod-Gauthier-Villars},
     address = {Montreuil},
     volume = {18},
     number = {1},
     year = {1984},
     mrnumber = {727603},
     zbl = {0572.92004},
     language = {fr},
     url = {http://www.numdam.org/item/M2AN_1984__18_1_87_0/}
}
TY  - JOUR
AU  - Joly, G.
AU  - Kernevez, J. P.
TI  - Apparition de motifs géométriques dans une membrane enzymatique
JO  - RAIRO. Analyse numérique
PY  - 1984
SP  - 87
EP  - 116
VL  - 18
IS  - 1
PB  - Centrale des revues, Dunod-Gauthier-Villars
PP  - Montreuil
UR  - http://www.numdam.org/item/M2AN_1984__18_1_87_0/
LA  - fr
ID  - M2AN_1984__18_1_87_0
ER  - 
%0 Journal Article
%A Joly, G.
%A Kernevez, J. P.
%T Apparition de motifs géométriques dans une membrane enzymatique
%J RAIRO. Analyse numérique
%D 1984
%P 87-116
%V 18
%N 1
%I Centrale des revues, Dunod-Gauthier-Villars
%C Montreuil
%U http://www.numdam.org/item/M2AN_1984__18_1_87_0/
%G fr
%F M2AN_1984__18_1_87_0
Joly, G.; Kernevez, J. P. Apparition de motifs géométriques dans une membrane enzymatique. RAIRO. Analyse numérique, Tome 18 (1984) no. 1, pp. 87-116. http://www.numdam.org/item/M2AN_1984__18_1_87_0/

[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.

[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

[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

[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 | Zbl

[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 | Zbl

[13] J. Hiernaux et T. Erneux, Chemical patterns in circular morphogenetic fields, Bull. Math. Biol., 41 (1979), 461-468. | MR

[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 | Zbl

[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 | Zbl

[19] G. Meuraut et J. C. Saut, Bifurcation and stability in a chemical system, J. Math. Anal, and Appi. 59 (1977), 69-91. | MR | Zbl

[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

[21] D. Henry, Geometrie theory of semilinear parabolie équations, lecture notes in Vlathematics n° 840, Springer-Verlag, NewYork, 1981. | MR | Zbl

[22] Kato T., Perturbation theory for linear operators (Springer-Verlag, New York, 1960). | Zbl

[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 | Zbl

[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

[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 | Zbl

[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

[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 | Zbl

[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

[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 | Zbl

[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 | Zbl