On a Cycle in a 5-Dimensional Circular Gene Network Model

N. B. Ayupova; V. P. Golubyatnikov

doi:10.1134/S1990478921030029

On a Cycle in a 5-Dimensional Circular Gene Network Model

Research output: Contribution to journal › Article › peer-review

Abstract

The necessary and sufficient conditions are obtained for the uniqueness of a cycle in thephase portrait of a piecewise linear dynamical system that simulates functioning a gene networkwith five components regulated by negative feedbacks only. We describe the behavior oftrajectories of this system in the invariant domain homeomorphic to a torus and prove thestability of this cycle.

Translated title of the contribution	Об одном цикле в пятимерной модели кольцевой генной сети
Original language	English
Article number	2
Pages (from-to)	376-383
Number of pages	8
Journal	Journal of Applied and Industrial Mathematics
Volume	15
Issue number	3
DOIs	https://doi.org/10.1134/S1990478921030029
Publication status	Published - Aug 2021

Keywords

circular gene network model
cycle
fixed point
invariant domain
monotonicity
negative feedback
phase portrait
piecewise-linear dynamical system
Poincaré map
stability

OECD FOS+WOS

1.01 MATHEMATICS
2.03 MECHANICAL ENGINEERING

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title = "On a Cycle in a 5-Dimensional Circular Gene Network Model",

abstract = "The necessary and sufficient conditions are obtained for the uniqueness of a cycle in thephase portrait of a piecewise linear dynamical system that simulates functioning a gene networkwith five components regulated by negative feedbacks only. We describe the behavior oftrajectories of this system in the invariant domain homeomorphic to a torus and prove thestability of this cycle.",

keywords = "circular gene network model, cycle, fixed point, invariant domain, monotonicity, negative feedback, phase portrait, piecewise-linear dynamical system, Poincar{\'e} map, stability",

author = "Ayupova, {N. B.} and Golubyatnikov, {V. P.}",

note = "Funding Information: The authors were supported by the State Task to the Sobolev Institute of Mathematics (project no. 0314–2019–0011). Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

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AB - The necessary and sufficient conditions are obtained for the uniqueness of a cycle in thephase portrait of a piecewise linear dynamical system that simulates functioning a gene networkwith five components regulated by negative feedbacks only. We describe the behavior oftrajectories of this system in the invariant domain homeomorphic to a torus and prove thestability of this cycle.

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KW - cycle

KW - fixed point

KW - invariant domain

KW - monotonicity

KW - negative feedback

KW - phase portrait

KW - piecewise-linear dynamical system

KW - Poincaré map

KW - stability

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ER -

On a Cycle in a 5-Dimensional Circular Gene Network Model

Abstract

Keywords

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