Email this article Structure of the Phase Portrait of a Piecewise-Linear Dynamical System
- Authors: Ayupova N.B.1,2, Golubyatnikov V.P.1,3
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Yakovlev Novosibirsk Military Institute
- Issue: Vol 13, No 4 (2019)
- Pages: 606-611
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213259
- DOI: https://doi.org/10.1134/S1990478919040033
- ID: 213259
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Abstract
We consider some piecewise linear 4-dimensional dynamical system that models a gene network regulated by one negative feedback and three positive feedbacks. Glass and Pasternack described the conditions for the existence of a stable cycle in this model. We construct an invariant piecewise linear surface with nontrivial link with the Glass-Pasternack cycle outside the attraction domain of this stable cycle in the phase portrait of this system.
About the authors
N. B. Ayupova
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: ayupova@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 1, Novosibirsk, 630090
V. P. Golubyatnikov
Sobolev Institute of Mathematics; Yakovlev Novosibirsk Military Institute
Author for correspondence.
Email: glbtn@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Kluch-Kamyshenskoe Plato 6/2, Novosibirsk, 630114
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