S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Existence and Stability of the Relaxation Cycle in a Mathematical Repressilator Model”, Mat. Zametki, 101:1 (2017), 58–76; Math. Notes, 101:1 (2017), 71

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Matematicheskie Zametki, 2017, Volume 101, Issue 1, Pages 58–76
DOI: https://doi.org/10.4213/mzm11039 (Mi mzm11039)

This article is cited in 12 scientific papers (total in 12 papers)

Existence and Stability of the Relaxation Cycle in a Mathematical Repressilator Model

S. D. Glyzin^a, A. Yu. Kolesov^a, N. Kh. Rozov^b

^a P.G. Demidov Yaroslavl State University
^b Lomonosov Moscow State University

Full-text PDF (594 kB) Citations (12)

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DOI: https://doi.org/10.4213/mzm11039

Abstract: 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.

Funding agency	Grant number
Russian Foundation for Basic Research	15-01-04066а

Received: 07.12.2015
Revised: 05.03.2016

English version:
Mathematical Notes, 2017, Volume 101, Issue 1, Pages 71–86
DOI: https://doi.org/10.1134/S0001434617010072

Bibliographic databases:

Document Type: Article

UDC: 517.926

Language: Russian

Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Existence and Stability of the Relaxation Cycle in a Mathematical Repressilator Model”, Mat. Zametki, 101:1 (2017), 58–76; Math. Notes, 101:1 (2017), 71–86

Citation in format AMSBIB

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https://doi.org/10.4213/mzm11039

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This publication is cited in the following 12 articles:

V. P. Golubyatnikov, E. A. Tatarinova, “Mathematical and Numerical Modeling of the Pluripotency Gene Network Dynamics”, Numer. Analys. Appl., 18:1 (2025), 36
V. P. Golubyatnikov, “O needinstvennosti tsiklov v trekhmernykh modelyakh koltsevykh gennykh setei”, Chelyab. fiz.-matem. zhurn., 9:1 (2024), 23–34
A. V. Glubokikh, V. P. Golubyatnikov, “On nonlocal oscillations in 3D models of circular gene networks”, J. Appl. Industr. Math., 18:2 (2024), 246–252
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “On a mathematical model of the repressilator”, St. Petersburg Math. J., 33:5 (2022), 797–828
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “A new approach to gene network modeling”, Autom. Control Comp. Sci., 54:7 (2020), 655–684
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Quasi-stable solutions of the genetic networks models”, International Conference on Computer Simulation in Physics and Beyond, Journal of Physics Conference Series, 1163, ed. L. Shchur, IOP Publishing Ltd, 2019, UNSP 012070
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Novyi podkhod k modelirovaniyu gennykh setei”, Model. i analiz inform. sistem, 26:3 (2019), 365–404
Z. Liu, X. Zhang, X. Wang, “Global exponential stability of delayed coupled repressilators in artificial oscillatory networks”, 2019 IEEE 58Th Conference on Decision and Control (Cdc), IEEE Conference on Decision and Control, IEEE, 2019, 1907–1912
Zexing Liu, Xian Zhang, Xin Wang, 2019 IEEE 58th Conference on Decision and Control (CDC), 2019, 1907
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Quasi-stable structures in circular gene networks”, Comput. Math. Math. Phys., 58:5 (2018), 659–679
V. P. Golubyatnikov, V. V. Ivanov, “Edinstvennost i ustoichivost tsikla v trekhmernykh blochno-lineinykh modelyakh koltsevykh gennykh setei”, Sib. zhurn. chist. i prikl. matem., 18:4 (2018), 19–28
V. P. Golubyatnikov, N. E. Kirillova, “On cycles in models of functioning of circular gene networks”, J. Math. Sci., 246:6 (2020), 779–787

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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