On multidimensional models of gene networks
Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 3, pp. 13-18.

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain sufficient conditions for the existence of closed trajectories in the odd-dimensional nonlinear dynamical systems that model gene networks with negative feedback.
Keywords: gene networks, negative feedback, nonlinear dynamical systems, stationary points, periodic trajectories.
@article{SJIM_2010_13_3_a2,
     author = {V. P. Golubyatnikov and I. V. Golubyatnikov},
     title = {On multidimensional models of gene networks},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {13--18},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2010_13_3_a2/}
}
TY  - JOUR
AU  - V. P. Golubyatnikov
AU  - I. V. Golubyatnikov
TI  - On multidimensional models of gene networks
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2010
SP  - 13
EP  - 18
VL  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2010_13_3_a2/
LA  - ru
ID  - SJIM_2010_13_3_a2
ER  - 
%0 Journal Article
%A V. P. Golubyatnikov
%A I. V. Golubyatnikov
%T On multidimensional models of gene networks
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2010
%P 13-18
%V 13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2010_13_3_a2/
%G ru
%F SJIM_2010_13_3_a2
V. P. Golubyatnikov; I. V. Golubyatnikov. On multidimensional models of gene networks. Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 3, pp. 13-18. http://geodesic.mathdoc.fr/item/SJIM_2010_13_3_a2/

[1] Gaidov Yu. A., Golubyatnikov V. P., “O nekotorykh nelineinykh dinamicheskikh sistemakh, modeliruyuschikh nesimmetrichnye gennye seti”, Vestnik NGU. Ser. mat., 7:2 (2007), 8–17

[2] Golubyatnikov V. P., Kleschev A. G., Klescheva K. A., Kudryavtseva A. V., “Issledovanie fazovykh portretov trekhmernykh modelei gennykh setei”, Sib. zhurn. industr. matematiki, 9:1 (2006), 75–84 | MR

[3] Golubyatnikov V. P., Gaidov Yu. A., Kleshchev A. G., Volokitin E. P., “Modeling of asymmetric gene networks functioning with different types of regulation”, Biophysics, 51:1 (2006), 61–65 | DOI

[4] Likhoshvai V. A., Golubyatnikov V. P., Demidenko G. V., Evdokimov A. A., Fadeev S. I., “Teoriya gennykh setei”, Sistemnaya kompyuternaya biologiya. Integratsionnye proekty, 14 (2008), 395–480

[5] Golubyatnikov V. P., Likhoshvai V. A., Volokitin E. P., Gaidov Yu. A., Osipov A. F., “Periodic trajectories and Andronov–Hopf bifurcations in models of gene networks”, Bioinformatics of Genome Regulation and Structure, v. II, Springer Verl., N.Y., 2006, 405–414

[6] Volokitin E. P., Treskov S. A., “Bifurkatsiya Andronova–Khopfa v modeli gipoteticheskikh gennykh setei”, Sib. zhurn. industr. matematiki, 8:1 (2005), 30–40 | MR

[7] Gaidov Yu. A., “Ob ustoichivosti periodicheskikh traektorii v nekotorykh modelyakh gennykh setei”, Sib. zhurn. industr. matematiki, 11:1 (2008), 57–62 | MR

[8] Likhoshvai V. A. Matushkin Yu. G., Fadeev S. I., “Zadachi teorii funktsionirovaniya gennykh setei”, Sib. zhurn. industr. matematiki, 6:2 (2003), 64–80 | MR | Zbl

[9] Hastings S., Tyson J., Webster D., “Existence of periodic solutions for negative feedback cellular control systems”, J. Differential Equations, 25 (1977), 39–64 | DOI | MR | Zbl

[10] Elowitz M. B., Leibler S., “A synthetic oscillatory network of transcription regulators”, Nature, 403 (2000), 335–338 | DOI

[11] Gardner T. S., Cantor C. R., Collins J. J., “Construction of a genetic toggle switch in Escherichia coli”, Nature, 403 (2000), 339–342 | DOI

[12] Golubyatnikov V. P., Likhoshvai V. A., Gaidov Yu. A., Kleshchev A. G., Lashina E. A., “Regular and chaotic dynamics in the gene networks modeling”, Proc. Internat. Conf. “Human and Computers-2005”, Univ. of Aizu, Aizu-Wakamatsu, 7–12