Abstract:
We obtain conditions of uniqueness of a cycle in phase portrait of one piecewise linear dynamical system which simulates functioning of a circular gene network with five components regulated by neagtive feedbacks only. We describe behavior of trajectories of this system in its invariant toric domain, and show stability of that cycle.
Citation:
N. B. Ayupova, V. P. Golubyatnikov, “On stucture of phase portrait of one 5-dimensional gene network model”, Sib. Zh. Ind. Mat., 24:3 (2021), 19–29
\Bibitem{AyuGol21}
\by N.~B.~Ayupova, V.~P.~Golubyatnikov
\paper On stucture of phase portrait of one 5-dimensional gene network model
\jour Sib. Zh. Ind. Mat.
\yr 2021
\vol 24
\issue 3
\pages 19--29
\mathnet{http://mi.mathnet.ru/sjim1139}
\crossref{https://doi.org/10.33048/SIBJIM.2021.24.302}
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https://www.mathnet.ru/eng/sjim1139
https://www.mathnet.ru/eng/sjim/v24/i3/p19
This publication is cited in the following 4 articles:
V. P. Golubyatnikov, “O needinstvennosti tsiklov v trekhmernykh modelyakh koltsevykh gennykh setei”, Chelyab. fiz.-matem. zhurn., 9:1 (2024), 23–34
A. V. Glubokikh, V. P. Golubyatnikov, “On nonlocal oscillations in 3D models of circular gene networks”, J. Appl. Industr. Math., 18:2 (2024), 246–252
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
V. V. Ivanov, “Prityagivayuschii predelnyi tsikl modeli nechetnomernoi koltsevoi gennoi seti”, Sib. zhurn. industr. matem., 25:3 (2022), 25–32
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