V. P. Golubyatnikov, O. A. Podkolodnaya, N. L. Podkolodnyi, N. B. Ayupova, N. E. Kirillova, E. V. Yunosheva, “Conditions of existence of cycles in two basic models of circadian oscillator of Mammalians ”, Sib. Zh. Ind. Mat., 2021, Volume 24, Number 4,Pages <nobr>39

This article is cited in 1 paper

Conditions of existence of cycles in two basic models of circadian oscillator of Mammalians

V. P. Golubyatnikov^ab, O. A. Podkolodnaya^c, N. L. Podkolodnyi^cd, N. B. Ayupova^ab, N. E. Kirillova^a, E. V. Yunosheva^b

^a Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
^b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
^c Institute of Cytology and Genetics SB RAS, pr. Acad. Koptyuga 2, Novosibirsk 630090, Russia
^d Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentyeva 6, Novosibirsk 630090, Russia

Abstract: We construct two non-linear dynamcal systems as models of symplest circadian oscillator's functioning. Conditions of uniqueness of equilibrium point of these systems are described as well as conditions of existence of cycles in their phase portraits.

Keywords: circadian oscillator, gene network, mathematical model, non-linear dynamical systems, positive and negative feedbacks, hyperbolic equilibrium point, phase portrait, cycle. .

UDC: УДК 517.938

Received: 30.08.2021
Revised: 30.08.2021
Accepted: 21.10.2021

DOI: 10.33048/SIBJIM.2021.24.403