This article is cited in 7 papers

On invariant surfaces in gene network models

N. E. Kirillova

Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia

Abstract: We construct an invariant two-dimensional surface in the phase portrait of a certain six-dimensional dynamical system which is considered as a model for the circular gene network functioning. This invariant surface contains an equilibrium point $S_0$ of the system, and if $S_0$ is hyperbolic then this surface contains a cycle of the system. The conditions for the existence of a cycle of this and similar systems were obtained earlier.

Keywords: circular gene network model, phase portrait, cycle, hyperbolic equilibrium point, invariant surface. .

UDC: 514.745.82

Received: 12.06.2020
Revised: 09.08.2020
Accepted: 10.09.2020

DOI: 10.33048/SIBJIM.2020.23.405

 English version: Journal of Applied and Industrial Mathematics, 2020, 14:4, 666–671

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