Abstract:
We describe necessary and suffcient conditions for uniqueness and stability of a cycle in an invariant domain of phase portrait of one Glass-Pasternack type block-linear dynamical system that simulates functioning of one natural gene network. Existence of such a cycle, geometry and combinatorics of phase portraits of similar systems were studied in our previous publications.
Citation:
V. P. Golubyatnikov, L. S. Minushkina, “On uniqueness and stability of a cycle in one gene network”, Sib. Èlektron. Mat. Izv., 18:1 (2021), 464–473
\Bibitem{GolMin21}
\by V.~P.~Golubyatnikov, L.~S.~Minushkina
\paper On uniqueness and stability of a cycle in one gene network
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 1
\pages 464--473
\mathnet{http://mi.mathnet.ru/semr1373}
\crossref{https://doi.org/10.33048/semi.2021.18.032}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000651770300001}
Linking options:
https://www.mathnet.ru/eng/semr1373
https://www.mathnet.ru/eng/semr/v18/i1/p464
This publication is cited in the following 6 articles:
V. P. Golubyatnikov, “O needinstvennosti tsiklov v trekhmernykh modelyakh koltsevykh gennykh setei”, Chelyab. fiz.-matem. zhurn., 9:1 (2024), 23–34
V. P. Golubyatnikov, N. E. Kirillova, L. S. Minushkina, “Chislennoe i matematicheskoe modelirovanie gennoi seti s nelineinoi degradatsiei komponent”, Sib. zhurn. vychisl. matem., 27:1 (2024), 1–10
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
L. S. Minushkina, “Periodicheskie traektorii nelineinykh modelei koltsevykh gennykh setei”, Vladikavk. matem. zhurn., 25:4 (2023), 80–90
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
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
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