Geodesic
On some many-dimensional models of the functioning of gene networks
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 3-9.

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We obtain a sufficient condition for the nonuniqueness of cycles in some nonlinear dynamical systems considered as models of the functioning of gene networks. Some constructive methods of determination of these cycles and invariant surfaces containing these cycles are described as well.
Keywords: nonlinear dynamical systems, gene networks models, stationary points
Mots-clés : phase portraits, invariant domains, cycles. 
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A. A. Akinshin; V. P. Golubyatnikov; I. V. Golubyatnikov. On some many-dimensional models of the functioning of gene networks. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a0/

[1] Golubyatnikov V. P., Golubyatnikov I. V., “O mnogomernykh modelyakh funktsionirovaniya gennykh setei”, Sib. zhurn. industr. matematiki, 13:3 (2010), 13–18 | MR | Zbl

[2] Likhoshvai V. A., Golubyatnikov V. P., Demidenko G. V., Evdokimov A. A., Fadeev S.I., “Teoriya gennykh setei”, Sistemnaya kompyuternaya biologiya, Izd-vo SO RAN, Novosibirsk, 2008, 395–480

[3] Likhoshvai V. A., Matushkin Yu. G., Fadeev S. I., “Zadachi teorii funktsionirovaniya gennykh setei”, Molekulyarnaya biologiya, 35:6 (2001), 926–932

[4] Gaidov Yu. A., Golubyatnikov V. P., “On the existence and stability of cycles in gene networks with variable feedbacks”, Contemp. Math., 553 (2011), 61–74 | DOI | MR | Zbl

[5] Golubyatnikov V. P., Likhoshvai V. A., Ratushny A. V., “Existence of closed trajectories in 3-D gene networks”, J. 3-dimensional Images 3D Forum, 18:4 (2004), 96–101

[6] Golubyatnikov V. P., Golubyatnikov I. V., “On periodic trajectories in odd–dimensional gene networks models”, Russian J. Numer. Anal. Math. Modeling, 28:4 (2011), 397–412 | MR

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

[8] Akinshin A. A., Golubyatnikov V. P., “Tsikly v simmetrichnykh dinamicheskikh sistemakh”, Vestn. NGU, 12:2 (2012), 3–12

[9] 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. 8 Internat. Conf. “Human and Computers”, Aizu, Japan, 2005, 7–12

[10] Golubyatnikov V. P., Golubyatnikov I. V., Likhoshvai V. A., “O suschestvovanii i ustoichivosti tsiklov v pyatimernykh modelyakh gennykh setei”, Sib. zhurn. vychisl. matematiki, 13:4 (2010), 403–411

[11] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1979 | MR

[12] Akinshin A. A., “Computer analysis of phase portraits in gene networks models”, Young Scientists School on Bioinformatics (Novosibirsk, June 2012), Abstracts, 13

[13] Akinshin A. A., Golubyatnikov V. P., “On nonuniqueness of cycles in dissipative dynamical systems of chemical kinetics”, Proc. 6 Internat. Conf. “Solitons, Collapses and Turbulence” (Novosibirsk, June 2012), 71–72

[14] 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 Sci., Berlin, 2006, 405–414 | DOI

[15] Akinshin A. A., Golubyatnikov V. P., “Non-uniqueness of cycles in gene networks models”, 8 Internat. Conf. “Bioinformatics of Genome Regulation and Structure, System Biology” (Novosibirsk, June 2012), Abstracts, 28