This article is cited in 2 papers

On uniqueness of a cycle in one circular gene network model

V. P. Golubyatnikov^ab, L. S. Minushkina<sup>a

a</sup> Novosibirsk State University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We obtain conditions for uniqueness of a cycle in the phase portrait of a piecewise linear dynamical system of the Elowitz–Leibler type which simulates the functioning of a simplest circular gene network. We describe the behavior of trajectories of this system in the invariant toric neighborhood of the cycle.

Keywords: circular gene network, positive and negative feedbacks, block-linear dynamical system, invariant domain, Poincaré map, fixed point, cycle.

UDC: 514.745.82

Received: 18.01.2021
Revised: 25.06.2021
Accepted: 11.08.2021

DOI: 10.33048/smzh.2022.63.106

 English version: Siberian Mathematical Journal, 2022, 63:1, 79–86

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