V. P. Golubyatnikov, M. V. Kazantsev, “On one piecewise linear dynamical system which models a gene network with variable feedback”, Sib. J. Pure and Appl. Math., 2016, Volume 16, Issue 4,Pages <nobr>28

This article is cited in 3 papers

On one piecewise linear dynamical system which models a gene network with variable feedback

V. P. Golubyatnikov^ab, M. V. Kazantsev^c

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University
^c Altai State Technical University

Abstract: Discretization of phase portrait of one 3-dimensional biochemical kinetics dynamical system with piecewise linear right-hand sides of special form is constructed. We describe geometry of this phase portrait and construct there a piecewise linear invariant surface bounded by a stable cycle which is composed by eight rectilinear segments.

Keywords: gene network modeling, positive and negative feedbacks, phase portraits of dynamical systems, cycles, invariant surfaces, the Poincare map, projective transformations.

UDC: 514.745.82

Received: 07.06.2016

DOI: 10.17377/PAM.2016.16.404