N. B. Ayupova, V. P. Golubyatnikov, “A three-cell model of the initial stage of the development of one proneural cluster”, Sib. Zh. Ind. Mat., 2017, Volume 20, Number 2,Pages <nobr>15

This article is cited in 2 papers

A three-cell model of the initial stage of the development of one proneural cluster

N. B. Ayupova^ab, V. P. Golubyatnikov^ab

^a Sobolev Institute of Mathematics SB RAS, Acad. Koptyuga ave., 4, 630090 Novosibirsk
^b Novosibirsk State University, Pirogova str., 2, 630090 Novosibirsk

Abstract: We construct a $9$-dimensional nonlinear dynamical system modeling the initial stage of the interaction of three adjacent cells in a proneural cluster of Drosophila melanogaster. Conditions of existence of three stable equilibrium points in the phase portrait of this system are obtained, other equilibrium points are listed, a biological interpretation is given.

Keywords: nonlinear dynamical system, gene network, negative and positive feedback, phase portrait, equilibrium point, stability.

UDC: 573.2+57.017.64

Received: 30.06.2016

DOI: 10.17377/sibjim.2017.20.202