On existence of a cycle in one asymmetric model of a molecular repressilator
N.B. Ayupova1,2, V.P. Golubyatnikov1,2, M.V. Kazantsev3
1Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, Novosibirsk, Russia, 630090
2Novosibirsk State University, 1 Pirogova str., Novosibirsk, Russia, 630090
3Polzunov Altai State Technical University, Lenina avenue, 46, Barnaul, Altai region, Russian, 656038
Keywords: нелинейная динамическая система, модели генных сетей, дискретизация фазового портрета, гиперболические стационарные точки, циклы, теорема Брауэра о неподвижной точке, nonlinear dynamical systems, gene networks models, phase portrait's discretization, hyperbolic equilibrium points, cycles, Brower's fixed point theorem
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 C in the phase portrait of this system. An invariant neighborhood of C which retracts to C has been constructed.
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