Geodesic
The Andronov–Hopf bifurcation in a model of a hypothetical gene regulatory network
Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 1, pp. 30-40 Cet article a éte moissonné depuis la source Math-Net.Ru

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Stability of the limit cycles of small amplitude resulting from the Andronov–Hopf bifurcation is studied in a system of ordinary differential equations which describes the behavior of a hypothetical gene regulatory network. 
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E. P. Volokitin; S. A. Treskov. The Andronov–Hopf bifurcation in a model of a hypothetical gene regulatory network. Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 1, pp. 30-40. http://geodesic.mathdoc.fr/item/SJIM_2005_8_1_a3/

[1] Likhoshvai V. A., Matushkin Yu. G., Fadeev S. I., “Zadachi teorii funktsionirovaniya gennykh setei”, Sib. zhurn. industr. matematiki, 6:2(14) (2003), 64–80 | MR

[2] Fadeev S. I., Likhoshvai V. A., “O gipoteticheskikh gennykh setyakh”, Sib. zhurn. industr. matematiki, 6:3(15) (2003), 134–153 | MR | Zbl

[3] Golubyatnikov V. P., Makarov E. V., “Closed trajectories in the gene networks”, Proc. 4 Internat. Conf. on Bioinformatics of Genome Regulation and Structure, v. 2 (Novosibirsk, July 25–30, 2004), Novosibirsk, 2004, 42–45

[4] Volokitin E. P., “O predelnykh tsiklakh v prosteishei modeli gipoteticheskoi gennoi seti”, Sib. zhurn. industr. matematiki, 7:3(19) (2004), 57–65 | MR | Zbl

[5] Bellman R., Vvedenie v teoriyu matrits, Nauka, M., 1969 | MR | Zbl

[6] Kuznetsov Yu. A., Elements of Applied Bifurcation Theory, Springer-Verl., N. Y., 1995 | MR

[7] Kuznetsov Yu. A., “Numerical normalization techniques for all codim 2 bifurcations of equilibria in ODE's”, SIAM J. Numer. Anal., 30 (1999), 1104–1124 | DOI | MR

[8] Demidenko G. V., Kolchanov N. A., Likhoshvai V. A., Matushkin Yu. G., Fadeev S. I., “Matematicheskoe modelirovanie regulyarnykh konturov gennykh setei”, Zhurn. vychisl. matematiki i mat. fiziki, 44:12 (2004), 2276–2295 | MR | Zbl