Geodesic
Pattern formation caused by convective flows coming from the opposite directions
Matematičeskoe modelirovanie, Tome 16 (2004) no. 4, pp. 41-46 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that convective flows of the inhibitor variable coming from the opposite directions may cause violation of stability of the spatially uniform state. The conditions of the reaction-convection-diffusion instability are obtained which are the generalization of the Turing instability conditions for a reaction-diffusion system. These analytic results were confirmed by numeric simulations on the example of the Brusselator model. 
@article{MM_2004_16_4_a4,
     author = {A. A. Polezhaev},
     title = {Pattern formation caused by convective flows coming from the opposite directions},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {41--46},
     year = {2004},
     volume = {16},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_4_a4/}
}
TY  - JOUR
AU  - A. A. Polezhaev
TI  - Pattern formation caused by convective flows coming from the opposite directions
JO  - Matematičeskoe modelirovanie
PY  - 2004
SP  - 41
EP  - 46
VL  - 16
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MM_2004_16_4_a4/
LA  - ru
ID  - MM_2004_16_4_a4
ER  - 
%0 Journal Article
%A A. A. Polezhaev
%T Pattern formation caused by convective flows coming from the opposite directions
%J Matematičeskoe modelirovanie
%D 2004
%P 41-46
%V 16
%N 4
%U http://geodesic.mathdoc.fr/item/MM_2004_16_4_a4/
%G ru
%F MM_2004_16_4_a4
A. A. Polezhaev. Pattern formation caused by convective flows coming from the opposite directions. Matematičeskoe modelirovanie, Tome 16 (2004) no. 4, pp. 41-46. http://geodesic.mathdoc.fr/item/MM_2004_16_4_a4/

[1] Murray J. D., Mathematical biology, Springer-Verlag, Berlin, 1989, 760 pp. | MR

[2] Mbller S. C., Plesser Th., Spato-temporal organization in non-equilibrium systems, Project-Verlag, Dortmund, 1992, 428 pp.

[3] Turring A. M., “The chemical basis of morphogenesis”, Philos. Trans. R. Soc. Lond. B. Biol. Sci., 237 (1952), 37–72 | DOI

[4] Meinhardt H., Models of biological pattern formation, Academic Press, New York, 1982, 230 pp.

[5] Kondo S., Asai R., “Turing patterns in fish skin?”, Nature, 376 (1995), 765–768 | DOI

[6] Romanovskii Yu. M., Stepanova N. V., Chernavskii D. S., Matematicheskaya biofizika, Nauka, M., 1984, 304 pp. | MR | Zbl

[7] Lucas W. J., “Mechanism of acquisition of exogenous bicarbonate by internodal cells of Chara corallina”, Planta, 156 (1982), 181–192 | DOI

[8] Toko K., Chosa H., Yamafuji K., “Dissipative structure in the Characeae: Spatial pattern of proton flux as a dissipative structure in characean cells”, J. theor. Biol., 114 (1985), 127–175 | DOI

[9] Bulychev A. A., Polezhaev A. A., Zykov S. V., Pljusnina T. Yu., Riznichenko G. Yu., Rubin A. B., Janto B. W., Zykov V. S., Mbller S. C., “Light-triggered pH banding profile in Chara cells revealed with a scanning pH microprobe and its relation to self-organization phenomena”, J. theor. Biol., 212 (2001), 275–294 | DOI

[10] Rovinsky A. B., Menzinger M., “Chemical instability induced by a differential flow”, Phys. Rev. Lett., 69 (1992), 1193–1196 | DOI

[11] Lobanov A. M., Plyusnina T. Yu., Riznichenko G. Yu., Starozhilova T. K., Rubin A. B., “Vliyanie elektricheskogo polya na struktury v reaktsionno-diffuzionnoi sisteme”, Biofizika, 45 (2000), 495–502

[12] Nicolis G., Prigogine I., Self-organization in non-equilibrium systems, Wiley, N.Y., 1977, 512 pp. | MR | Zbl