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Title: Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback

Abstract

We construct a discretization of the phase portrait of a 3-dimensional dynamical system of biochemical kinetics with piecewise linear right-hand sides. We describe geometry of the phase portrait and construct an invariant piecewise linear surface bounded by a stable cycle of this system composed of eight linear segments.

Authors:
 [1];  [2]
  1. Sobolev Institute of Mathematics SB RAS (Russian Federation)
  2. I.I. Pozunov Altai State Technical University (Russian Federation)
Publication Date:
OSTI Identifier:
22771406
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 230; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; COMPUTERIZED SIMULATION; DYNAMICAL SYSTEMS; GENES; GEOMETRY; KINETICS; SURFACES; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Golubyatnikov, V. P., E-mail: glbtn@math.nsc.ru, and Kazantsev, M. V., E-mail: markynaz.astu@gmail.com. Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3725-0.
Golubyatnikov, V. P., E-mail: glbtn@math.nsc.ru, & Kazantsev, M. V., E-mail: markynaz.astu@gmail.com. Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback. United States. doi:10.1007/S10958-018-3725-0.
Golubyatnikov, V. P., E-mail: glbtn@math.nsc.ru, and Kazantsev, M. V., E-mail: markynaz.astu@gmail.com. Sun . "Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback". United States. doi:10.1007/S10958-018-3725-0.
@article{osti_22771406,
title = {Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback},
author = {Golubyatnikov, V. P., E-mail: glbtn@math.nsc.ru and Kazantsev, M. V., E-mail: markynaz.astu@gmail.com},
abstractNote = {We construct a discretization of the phase portrait of a 3-dimensional dynamical system of biochemical kinetics with piecewise linear right-hand sides. We describe geometry of the phase portrait and construct an invariant piecewise linear surface bounded by a stable cycle of this system composed of eight linear segments.},
doi = {10.1007/S10958-018-3725-0},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 1,
volume = 230,
place = {United States},
year = {2018},
month = {4}
}