TY - JOUR

T1 - On Conditions for the Existence of Cycles in Two Models of a Circadian Oscillator of Mammals

AU - Golubyatnikov, V. P.

AU - Podkolodnaya, O. A.

AU - Podkolodnyy, N. L.

AU - Ayupova, N. B.

AU - Kirillova, N. E.

AU - Yunosheva, E. V.

N1 - Funding Information: The authors were supported within the framework of the State Contract of Institute of Cytology and Genetics (project no. FWNR–2022–0020), the State Contract of Institute of Computational Mathematics and Mathematical Geophysics (project no. 0251–2021–0004), the State Contract of Sobolev Institute of Mathematics (project no. FWNF–2022–0009), and partially by the Russian Foundation for Basic Research (project no. 20–31–90011). Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/11

Y1 - 2021/11

N2 - We construct two nonlinear dynamical systems of the functioning simplest circadianoscillator. Some conditions of the uniqueness of the equilibrium point of these systems aredescribed as well as the conditions for the existence of cycles in their phase portraits.

AB - We construct two nonlinear dynamical systems of the functioning simplest circadianoscillator. Some conditions of the uniqueness of the equilibrium point of these systems aredescribed as well as the conditions for the existence of cycles in their phase portraits.

KW - circadian oscillator

KW - gene network

KW - hyperbolic equilibrium point

KW - limit cycle

KW - mathematical model

KW - nonlinear dynamical system

KW - phase portrait

KW - positive and negative feedback

UR - http://www.scopus.com/inward/record.url?scp=85133968780&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/6101768f-b2bf-31a1-914d-98406f7e223c/

U2 - 10.1134/S1990478921040037

DO - 10.1134/S1990478921040037

M3 - Article

AN - SCOPUS:85133968780

VL - 15

SP - 597

EP - 608

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 4

ER -