Monotonicity of the Poincaré Mapping in Some Models of Circular Gene Networks

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Monotonicity of the Poincaré Mapping in Some Models of Circular Gene Networks. / Golubyatnikov, V. P.; Minushkina, L. S.

In: Journal of Applied and Industrial Mathematics, Vol. 13, No. 3, 01.07.2019, p. 472-479.

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

BibTeX

@article{c2fd27bd9f784123b0e3c90e0cd574a1,

title = "Monotonicity of the Poincar{\'e} Mapping in Some Models of Circular Gene Networks",

abstract = "We obtain some sufficient conditions for the existence of a periodic trajectory of the Elowitz-Leibler type piecewise linear dynamical system that simulates a simplest nonsymmetric circular gene network. We prove the monotonicity of the corresponding Poincar{\'e} mapping and construct an invariant toric neighborhood of this cycle.",

keywords = "circular gene network, cycle, invariant domain, piecewise-linear dynamical system, Poincar{\'e} mapping, positive and negative feedbacks",

author = "Golubyatnikov, {V. P.} and Minushkina, {L. S.}",

note = "Publisher Copyright: {\textcopyright} 2019, Pleiades Publishing, Ltd.",

year = "2019",

month = jul,

day = "1",

doi = "10.1134/S1990478919030086",

language = "English",

volume = "13",

pages = "472--479",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Monotonicity of the Poincaré Mapping in Some Models of Circular Gene Networks

AU - Golubyatnikov, V. P.

AU - Minushkina, L. S.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - We obtain some sufficient conditions for the existence of a periodic trajectory of the Elowitz-Leibler type piecewise linear dynamical system that simulates a simplest nonsymmetric circular gene network. We prove the monotonicity of the corresponding Poincaré mapping and construct an invariant toric neighborhood of this cycle.

AB - We obtain some sufficient conditions for the existence of a periodic trajectory of the Elowitz-Leibler type piecewise linear dynamical system that simulates a simplest nonsymmetric circular gene network. We prove the monotonicity of the corresponding Poincaré mapping and construct an invariant toric neighborhood of this cycle.

KW - circular gene network

KW - cycle

KW - invariant domain

KW - piecewise-linear dynamical system

KW - Poincaré mapping

KW - positive and negative feedbacks

UR - http://www.scopus.com/inward/record.url?scp=85071434868&partnerID=8YFLogxK

U2 - 10.1134/S1990478919030086

DO - 10.1134/S1990478919030086

M3 - Article

AN - SCOPUS:85071434868

VL - 13

SP - 472

EP - 479

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 3

ER -

ID: 21472478