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This article is cited in 11 scientific papers (total in 11 papers)
On existence of a cycle in one asymmetric model of a molecular repressilator
N. B. Ayupovaab, V. P. Golubyatnikovab, M. V. Kazantsevc a Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, Novosibirsk, 630090, Russia
b Novosibirsk State University, 2 Pirogova str., Novosibirsk, 630090, Russia
c Polzunov Altai State Technical University, Lenina avenue, 46, Barnaul, Altai region, 656038, Russia
Abstract:
We consider a nonlinear $6$-dimensional dynamic system which is a model of functioning of one simple molecular repressilator and find sufficient conditions of existence of a cycle $\mathcal C$ in the phase portrait of this system. An invariant neighborhood of $\mathcal C$ which retracts to $\mathcal C$ has been constructed.
Key words:
nonlinear dynamical systems, gene networks models, phase portrait's discretization, hyperbolic equilibrium points, cycles, Brower's fixed point theorem.
Received: 22.09.2016 Revised: 26.12.2016
Citation:
N. B. Ayupova, V. P. Golubyatnikov, M. V. Kazantsev, “On existence of a cycle in one asymmetric model of a molecular repressilator”, Sib. Zh. Vychisl. Mat., 20:2 (2017), 121–129; Num. Anal. Appl., 10:2 (2017), 101–107
Linking options:
https://www.mathnet.ru/eng/sjvm640 https://www.mathnet.ru/eng/sjvm/v20/i2/p121
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Abstract page: | 270 | Full-text PDF : | 26 | References: | 33 | First page: | 18 |
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