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

V. P. Golubyatnikov,O. A. Podkolodnaya,N. L. Podkolodnyy,N. B. Ayupova, N. E. Kirillova, E. V. Yunosheva

Journal of Applied and Industrial Mathematics（2022）

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摘要

We construct two nonlinear dynamical systems of the functioning simplest circadian oscillator. Some conditions of the uniqueness of the equilibrium point of these systems are described as well as the conditions for the existence of cycles in their phase portraits.

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关键词

circadian oscillator, gene network, mathematical model, nonlinear dynamical system, positive and negative feedback, hyperbolic equilibrium point, phase portrait, limit cycle

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