This article is cited in 7 papers

Monotonicity of the Poincaré mapping in some models of circular gene networks

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

a</sup> Sobolev Institute of Mathematics SB RAS pr. Akad. Koptyuga 4, 630090 Novosibirsk
^b Novosibirsk State University, ul. Pirogova 1, 630090 Novosibirsk

Abstract: We obtain some sufficient conditions for the existence of a periodic trajectory of the Elowitz–Leibler type piecewise linear dynamical system that simulates a simplest nonsymmetric circular gene network. We prove the monotonicity of the corresponding Poincaré mapping and construct an invariant toric neighborhood of this cycle.

Keywords: circular gene network, positive and negative feedbacks, piecewise-linear dynamical system, invariant domain, Poincaré mapping, cycle.

UDC: 514.745.82

Received: 29.11.2018
Revised: 16.04.2019
Accepted: 13.06.2019

DOI: 10.33048/sibjim.2019.22.304

 English version: Journal of Applied and Industrial Mathematics, 2019, 13:3, 472–479

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