On some multidimensional models of gene network functioning
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We obtain some sufficient conditions for the nonuniqueness of cycles in nonlinear dynamical systems considered as the models of gene network functioning. The constructive methods for the determination of these cycles and the invariant surfaces containing the mare described as well.
Keywordsnonlinear dynamical system gene network model phase portrait invariant domain equilibrium point cycle
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- 2.V. A. Likhoshvai, V. P. Golubyatnikov, G. V. Demidenko, A. A. Evdokimov, and S. I. Fadeev, “Gene Network Theory,” in Computer Systemic Biology (Izd. Sibirsk. Otdel. Ross. Akad. Nauk, Novosibirsk, 2008), pp. 395–480.Google Scholar
- 5.V. P. Golubyatnikov, V. A. Likhoshvai, and A. V. Ratushny, “Existence of Closed Trajectories in 3-D Gene Networks,” J. 3-Dimensional Images 3D Forum 18(4), 96–101 (2004).Google Scholar
- 7.E. P. Volokitin and S. A. Treskov, “The Andronov-Hopf Bifurcation in a Model of a Hypothetical Gene Regulatory Network,” Sibirsk. Zh. Industr. Mat. 8(1), 30–40 (2005) [J. Appl. Indust. Math. 1 (1), 127–136 (2007)].Google Scholar
- 8.A. A. Akinshin and V. P. Golubyatnikov, “Cycles in Symmetrical Dynamic Systems,” Vestnik Novosib. Gos. Univ. No. 2, 3–12 (2012).Google Scholar
- 9.V. P. Golubyatnikov, V. A. Likhoshvai, Yu. A. Gaidov, A. G. Kleshchev, and E. A. Lashina, “Regular and Chaotic Dynamics in the Gene Networks Modeling,” in Proceedings of the 8 International Conference “Human and Computers,” Aizu, Japan, 2005 (Aizu, 2005), pp. 7–12.Google Scholar
- 10.V. P. Golubyatnikov, I. V. Golubyatnikov, and V. A. Likhoshvai, “On the Existence and Stability of Cycles in Five-Dimensional Models of Gene Networks,” Sibirsk. Zh. Vychisl. Mat. 13(4), 403–411 (2010) [Numerical Anal. Appl. 3 (4), 329–335 (2010)].Google Scholar
- 12.A. A. Akinshin, “Computer Analysis of Phase Portraits in Gene Network Models,” in Young Scientists School on Bioinformatics, Novosibirsk, June 2012: Abstracts (Inst. Tsitolog. Genet., Novosibirsk, 2012), p. 13.Google Scholar
- 13.A. A. Akinshin and V. P. Golubyatnikov, “On Nonuniqueness of Cycles in Dissipative Dynamical Systems of Chemical Kinetics,” in Proceedings of the 6th International Conference “Solitons, Collapses and Turbulence,” Novosibirsk, June 2012 (Inst. Cytology and Genetics, Novosibirsk, 2012), p. 71–72.Google Scholar
- 15.A. A. Akinshin and V. P. Golubyatnikov, “Nonuniqueness of Cycles in Gene Networks Models,” in 8 International Conference “Bioinformatics of Genome Regulation and Structure, System Biology,” Novosibirsk, June 2012: Abstracts (Inst. Tsitolog. Genet., Novosibirsk, 2012), p. 28.Google Scholar