V. P. Golubyatnikov, N. E. Kirillova, “On cycles in models of functioning of circular gene networks”, Sib. J. Pure and Appl. Math., 2018, Volume 18, Issue 1,Pages <nobr>54

This article is cited in 4 papers

On cycles in models of functioning of circular gene networks

V. P. Golubyatnikov^ab, N. E. Kirillova^b

^a Sobolev Institute of Mathematics SB RAS, 4, Akad. Koptyuga pr., Novosibirsk 630090, Russia
^b Novosibirsk State University, 1, Pirogova St., Novosibirsk 630090, Russia

Abstract: We study a phase portrait of a nonlinear 10-dimensional dynamical system describing a model of functioning of one circular gene network. We find sufficient conditions for the existence of a cycle in this phase portrait. For a similar 18-dimensional dynamical system, we find conditions for the existence of at least two cycles in its phase portrait.

Keywords: nonlinear dynamical systems, circular gene network, phase portraits, cycles, torus principle.

UDC: 514.745.82

Received: 29.05.2017

DOI: 10.17377/PAM.2018.18.5