TY - JOUR

T1 - Non-Uniqueness of Cycles in Piecewise-Linear Models of Circular Gene Networks

AU - Golubyatnikov, V. P.

AU - Gradov, V. S.

N1 - Funding Information: The work was partially supported by the Russian Foundation for Basic Research (project 18-01-00057) and the Program of Fundamental Scientific Research of the SB RAS no. I.1.5 (project 0314-2018-0011). Publisher Copyright: © 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/2

Y1 - 2021/2

N2 - We find conditions for existence of two cycles for a five-dimensional piecewise-lineardynamical system that models functioning of a circular gene network. Conditions for existence ofa cycle were obtained by the authors earlier. The phase portrait of a system is divided intosubdomains (or blocks). With the use of such a discretization, we construct a combinatorialscheme for passages of trajectories between blocks. For the second cycle, we show that sucha scheme depends on the parameters of a system.

AB - We find conditions for existence of two cycles for a five-dimensional piecewise-lineardynamical system that models functioning of a circular gene network. Conditions for existence ofa cycle were obtained by the authors earlier. The phase portrait of a system is divided intosubdomains (or blocks). With the use of such a discretization, we construct a combinatorialscheme for passages of trajectories between blocks. For the second cycle, we show that sucha scheme depends on the parameters of a system.

KW - cycles

KW - invariant domains

KW - nonlinear dynamical systems

KW - phase portraits

KW - valency of a block

UR - http://www.scopus.com/inward/record.url?scp=85103567573&partnerID=8YFLogxK

U2 - 10.1134/S1055134421010016

DO - 10.1134/S1055134421010016

M3 - Article

AN - SCOPUS:85103567573

VL - 31

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 1

ER -