This article is cited in 6 papers

Differentical equations, dynamical systems and optimal control

On uniqueness and stability of a cycle in one gene network

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

a</sup> Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
^b Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia

Abstract: We describe necessary and suffcient conditions for uniqueness and stability of a cycle in an invariant domain of phase portrait of one Glass-Pasternack type block-linear dynamical system that simulates functioning of one natural gene network. Existence of such a cycle, geometry and combinatorics of phase portraits of similar systems were studied in our previous publications.

Keywords: circular gene network, fixed points, cycles, piecewise linear dynamical systems, phase portraits, invariant domains, Poincaré map.

UDC: 514.745.82

MSC: 37N25

Received January 28, 2021, published April 27, 2021

Language: English

DOI: 10.33048/semi.2021.18.032

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