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., 2017, Volume 20, Number 2,Pages <nobr>121

This article is cited in 11 papers

On existence of a cycle in one asymmetric model of a molecular repressilator

N. B. Ayupova^ab, V. P. Golubyatnikov^ab, M. V. Kazantsev^c

^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.

UDC: 514.745.82

Received: 22.09.2016
Revised: 26.12.2016

DOI: 10.15372/SJNM20170201