Email this article Monotonicity of the Poincaré Mapping in Some Models of Circular Gene Networks
- Authors: Golubyatnikov V.P.1,2, Minushkina L.S.2
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 13, No 3 (2019)
- Pages: 472-479
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213221
- DOI: https://doi.org/10.1134/S1990478919030086
- ID: 213221
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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 Poincaré mapping and construct an invariant toric neighborhood of this cycle.
About the authors
V. P. Golubyatnikov
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: glbtn@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 1, Novosibirsk, 630090
L. S. Minushkina
Novosibirsk State University
Author for correspondence.
Email: l.minushkina@g.nsu.ru
Russian Federation, ul. Pirogova 1, Novosibirsk, 630090
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