N. B. Ayupova, V. P. Golubyatnikov, “On stucture of phase portrait of one 5-dimensional gene network model ”, Sib. Zh. Ind. Mat., 2021, Volume 24, Number 3,Pages <nobr>19

This article is cited in 4 papers

On stucture of phase portrait of one 5-dimensional gene network model

N. B. Ayupova^ab, V. P. Golubyatnikov^ab

^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: We obtain conditions of uniqueness of a cycle in phase portrait of one piecewise linear dynamical system which simulates functioning of a circular gene network with five components regulated by neagtive feedbacks only. We describe behavior of trajectories of this system in its invariant toric domain, and show stability of that cycle.

Keywords: circular gene network model, negative feedbacks, piecewise-linear dynamical systems, phase portrait, invariant domains, Poincaré mapping, monotonicity, fixed point, cycles, stability. .

UDC: 514.745.82

Received: 10.03.2021
Revised: 19.04.2021
Accepted: 24.06.2021

DOI: 10.33048/SIBJIM.2021.24.302