Abstract:
We obtain sufficient conditions for the existence and stability of closed trajectories in five-dimensional nonlinear dynamical systems which model gene networks with negative feedbacks.
Citation:
V. P. Golubyatnikov, I. V. Golubyatnikov, V. A. Likhoshvai, “On the existence and stability of cycles in five-dimensional models of gene networks”, Sib. Zh. Vychisl. Mat., 13:4 (2010), 403–411; Num. Anal. Appl., 3:4 (2010), 329–335
\Bibitem{GolGolLik10}
\by V.~P.~Golubyatnikov, I.~V.~Golubyatnikov, V.~A.~Likhoshvai
\paper On the existence and stability of cycles in five-dimensional models of gene networks
\jour Sib. Zh. Vychisl. Mat.
\yr 2010
\vol 13
\issue 4
\pages 403--411
\mathnet{http://mi.mathnet.ru/sjvm415}
\transl
\jour Num. Anal. Appl.
\yr 2010
\vol 3
\issue 4
\pages 329--335
\crossref{https://doi.org/10.1134/S199542391004004X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650410556}
Linking options:
https://www.mathnet.ru/eng/sjvm415
https://www.mathnet.ru/eng/sjvm/v13/i4/p403
This publication is cited in the following 18 articles:
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N. B. Ayupova, V. P. Golubyatnikov, “Ob odnom tsikle v pyatimernoi modeli koltsevoi gennoi seti”, Sib. zhurn. industr. matem., 24:3 (2021), 19–29
Lakhova T.N., Kazantsev V F., Lashin S.A., Matushkin Yu.G., “The Finding and Researching Algorithm For Potentially Oscillating Enzymatic Systems”, Vavilovskii Zhurnal Genet. Sel., 25:3 (2021), 318–330
N. B. Ayupova, V. P. Golubyatnikov, “On a Cycle in a 5-Dimensional Circular Gene Network Model”, J. Appl. Ind. Math., 15:3 (2021), 376
V. P. Golubyatnikov, V. S. Gradov, “Non-Uniqueness of Cycles in Piecewise-Linear Models of Circular
Gene Networks”, Sib. Adv. Math., 31:1 (2021), 1
V. P. Golubyatnikov, V. S. Gradov, “O needinstvennosti tsiklov v nekotorykh kusochno-lineinykh modelyakh koltsevykh gennykh setei”, Matem. tr., 23:1 (2020), 107–122
Likhoshvai V.A., Golubyatnikov V.P., Khlebodarova T.M., “Limit Cycles in Models of Circular Gene Networks Regulated By Negative Feedback Loops”, BMC Bioinformatics, 21:11, SI (2020), 255
V. P. Golubyatnikov, V. V. Ivanov, “Cycles in the odd-dimensional models of circular gene networks”, J. Appl. Industr. Math., 12:4 (2018), 648–657
N. B. Ayupova, V. P. Golubyatnikov, “A three-cell model of the initial stage of the development of one proneural cluster”, J. Appl. Industr. Math., 11:2 (2017), 168–173
N. B. Ayupova, V. P. Golubyatnikov, M. V. Kazantsev, “On existence of a cycle in one asymmetric model of a molecular repressilator”, Num. Anal. Appl., 10:2 (2017), 101–107
Golubyatnikov V.P., Bukharina T.A., Furman D.P., “a Model Study of the Morphogenesis of D-Melanogaster Mechanoreceptors: the Central Regulatory Circuit”, J. Bioinform. Comput. Biol., 13:1, SI (2015), 1540006
A. Yu. Gaidov, P. V. Golubyatnikov, Springer Proceedings in Mathematics & Statistics, 72, Geometry and its Applications, 2014, 225
A. A. Akinshin, V. P. Golubyatnikov, I. V. Golubyatnikov, “On some many-dimensional models of the functioning of gene networks”, J. Appl. Industr. Math., 7:3 (2013), 296–301
S. I. Fadeev, V. V. Kogai, V. V. Mironova, N. A. Omelyanchuk, V. A. Likhoshvai, “Mathematical modeling of matter distribution in cells assembling into a ring”, Num. Anal. Appl., 6:2 (2013), 151–162
Bukharina T.A., Golubyatnikov V.P., Golubyatnikov I.V., Furman D.P., “Model investigation of central regulatory contour of gene net of D. melanogaster macrochaete morphogenesis”, Russian Journal of Developmental Biology, 43:1 (2012), 49–53
A. A. Akinshin, V. P. Golubyatnikov, “Tsikly v simmetrichnykh dinamicheskikh sistemakh”, Vestn. NGU. Ser. matem., mekh., inform., 12:2 (2012), 3–12
T. A. Bukharina, V. P. Golubyatnikov, I. V. Golubyatnikov, D. P. Furman, “Mathematical modeling of the first phase of morphogenesis of mechanoreceptors in D. melanogaster”, J. Appl. Industr. Math., 6:2 (2012), 145–149