N. B. Ayupova, V. P. Golubyatnikov, L. S. Minushkina, “On invariant surfaces in phase portraits of circular gene networks models ”, Sib. Zh. Ind. Mat., 2022, Volume 25, Number 4,Pages <nobr>5

This article is cited in 2 papers

On invariant surfaces in phase portraits of circular gene networks models

N. B. Ayupova^a, V. P. Golubyatnikov^a, L. S. Minushkina^b

^a Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
^b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia

Abstract: For block-linear dynamical system of dimensions 3 and 4 considered as models of simplest circular gene networks, we find sufficient conditions of existence of invariant surfaces in their phase portraits. These surfaces contain periodic trajectories of the dynamical systems.

Keywords: block-linear dynamical systems, invariant domains, invariant surfaces, Poincaré map, fixed point, cycles, Grobman—Hartman theorem, Perron—Frobenius theorem. .

UDC: 517.938

Received: 25.04.2022
Revised: 25.04.2022
Accepted: 22.06.2022

DOI: 10.33048/SIBJIM.2021.25.401