Geodesic
Existence and Stability of the Relaxation Cycle in a Mathematical Repressilator Model
Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 58-76 Cet article a éte moissonné depuis la source Math-Net.Ru

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The three-dimensional nonlinear system of ordinary differential equations modeling the functioning of the simplest oscillatory genetic network, the so-called repressilator, is considered. The existence, asymptotics, and stability of the relaxation periodic motion in this system are studied.
Keywords: repressilator, genetic oscillator, relaxation cycle, stability, asymptotics. 
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     title = {Existence and {Stability} of the {Relaxation} {Cycle} in a {Mathematical} {Repressilator} {Model}},
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S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Existence and Stability of the Relaxation Cycle in a Mathematical Repressilator Model. Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 58-76. http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a4/

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

[2] A. N. Tikhonov, “Sistemy differentsialnykh uravnenii, soderzhaschie malye parametry pri proizvodnykh”, Matem. sb., 31 (73):3 (1952), 575–586 | MR | Zbl

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

[4] O. Buşe, A. Kuznetsov, R. A. Pérez, “Existence of limit cycles in the repressilator equations”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 19:12 (2009), 4097–4106 | DOI | MR | Zbl

[5] O. Buse, R. Pérez, A. Kuznetsov, “Dynamical properties of the repressilator model”, Phys. Rev. E, 81 (2010), 066206 | DOI | MR

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

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

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