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.
Citation:
V. P. Golubyatnikov, L. S. Minushkina, “Monotonicity of the Poincaré mapping in some models of circular gene networks”, Sib. Zh. Ind. Mat., 22:3 (2019), 39–47; J. Appl. Industr. Math., 13:3 (2019), 472–479
\Bibitem{GolMin19}
\by V.~P.~Golubyatnikov, L.~S.~Minushkina
\paper Monotonicity of the Poincar\'{e} mapping in some models of circular gene networks
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 3
\pages 39--47
\mathnet{http://mi.mathnet.ru/sjim1052}
\crossref{https://doi.org/10.33048/sibjim.2019.22.304
}
\elib{https://elibrary.ru/item.asp?id=41633441}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 3
\pages 472--479
\crossref{https://doi.org/10.1134/S1990478919030086}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071434868}
Linking options:
https://www.mathnet.ru/eng/sjim1052
https://www.mathnet.ru/eng/sjim/v22/i3/p39
This publication is cited in the following 8 articles:
Vladimir P. Golubyatnikov, Natalia B. Ayupova, Natalia E. Bondarenko, Alina V. Glubokikh, “Hidden attractors and nonlocal oscillations in gene networks models”, Russian Journal of Numerical Analysis and Mathematical Modelling, 39:2 (2024), 75
V. P. Golubyatnikov, A. A. Akinshin, N. B. Ayupova, L. S. Minushkina, “Stratifications and foliations in phase portraits of gene network models”, Vestn. VOGiS, 26:8 (2023), 758
V. P. Golubyatnikov, L. S. Minushkina, “On uniqueness of a cycle in one circular gene network model”, Siberian Math. J., 63:1 (2022), 79–86
N. B. Ayupova, V. P. Golubyatnikov, L. S. Minushkina, “Ob invariantnykh poverkhnostyakh v fazovykh portretakh modelei koltsevykh gennykh setei”, Sib. zhurn. industr. matem., 25:4 (2022), 5–13
N. B. Ayupova, V. P. Golubyatnikov, L. S. Minushkina, “On Invariant Surfaces in the Phase Portraits of Models of Circular Gene Networks”, J. Appl. Ind. Math., 16:4 (2022), 589
V. P. Golubyatnikov, L. S. Minushkina, “On Uniqueness and Stability of a Cycle in One Gene Network”, Sib. Electron. Math. Rep., 18 (2021), 464–473
V. A. Likhoshvai, V. P. Golubyatnikov, T. M. Khlebodarova, “Limit cycles in models of circular gene networks regulated by negative feedback loops”, BMC Bioinformatics, 21:11, SI (2020), 255
R. Katz, M. Margaliot, E. Fridman, “Entrainment to subharmonic trajectories in oscillatory discrete-time systems”, Automatica, 116 (2020), 108919
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