Mots-clés : cycles
@article{VNGU_2018_18_3_a2,
author = {V. P. Golubyatnikov and V. V. Ivanov and L. S. Minushkina},
title = {On existence of a cycle in one asymmetric gene network model},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {27--35},
year = {2018},
volume = {18},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VNGU_2018_18_3_a2/}
}
TY - JOUR AU - V. P. Golubyatnikov AU - V. V. Ivanov AU - L. S. Minushkina TI - On existence of a cycle in one asymmetric gene network model JO - Sibirskij žurnal čistoj i prikladnoj matematiki PY - 2018 SP - 27 EP - 35 VL - 18 IS - 3 UR - http://geodesic.mathdoc.fr/item/VNGU_2018_18_3_a2/ LA - ru ID - VNGU_2018_18_3_a2 ER -
%0 Journal Article %A V. P. Golubyatnikov %A V. V. Ivanov %A L. S. Minushkina %T On existence of a cycle in one asymmetric gene network model %J Sibirskij žurnal čistoj i prikladnoj matematiki %D 2018 %P 27-35 %V 18 %N 3 %U http://geodesic.mathdoc.fr/item/VNGU_2018_18_3_a2/ %G ru %F VNGU_2018_18_3_a2
V. P. Golubyatnikov; V. V. Ivanov; L. S. Minushkina. On existence of a cycle in one asymmetric gene network model. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 3, pp. 27-35. http://geodesic.mathdoc.fr/item/VNGU_2018_18_3_a2/
[1] A. A. Akinshin, “Andronov-Hopf bifurcation for some nonliner delayed argument equations”, Sib. Zh. Ind. Mat., 16:3 (2013), 3–15 (in Russian) | MR | Zbl
[2] A. A. Akinshin, V. P. Golubyatnikov, “Cycles in symmetric dynamical systems”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 12:2 (2012), 3–12 (in Russian) | Zbl
[3] N. Ayupova B., V. P. Golubyatnikov, “On uniqueness of a cycle in an asymmetric three-dimensional model of a molecular repressilator”, J. Appl. Ind. Math., 8:2 (2014), 1–6 | DOI | MR | MR | Zbl
[4] V. P. Golubyatnikov, A. E. Kalenykh, “Structure of phase portraits of nonlinear dynamical systems”, J. of Math. Sci., 215:4 (2016), 475–483 | DOI | MR | Zbl
[5] A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “Periodic solutions of the travalling waves type in circuler gene networks”, Izv. Math., 80:3 (2016), 523–548 | DOI | DOI | MR | Zbl
[6] Glass L., Pasternack J. S., “Stable Oscillations in Mathematical Models of Biological Control Systems”, J. of Math. Biology, 6 (1978), 207–223 | DOI | MR | Zbl
[7] Elowitz M. B., Leibler S., “A Synthetic Oscillatory Network of Transcriptional Regulators”, Nature, 403 (2000), 335–338 | DOI
[8] V. A. Likhoshvai, V. P. Golubyatnikov, G. V. Demidenko, A. A. Evdokimov, S. I. Fadeev, “Gene networks theory”, System computational biology, Siberian Branch of RAS, Novosibirsk, 2008, 395–480 (in Russian)
[9] G. Yu. Riznichenko, Lectures on mathematical models in biology, RChD, Izhevsk, 2011 (in Russian)
[10] Hastings S., Tyson J. J., Webster D., “Existence of Periodic Solutions for Negative Feedbacks Cellular Control Systems”, Differ. Equ., 25 (1977), 39–64 | DOI | MR | Zbl
[11] E. P. Volokitin, “On limit cycles in a simple gene network model”, Sib. Zh. Ind. Mat., 7:3 (2004), 57–65 (in Russian) | MR
[12] Gaidov Yu. A., Golubyatnikov V. P., Kleshchev A. G., Volokitin E. P., “Modeling of Asymmetric Gene Networks Functioning with Different Types of Regulation”, Biophysics, 51, Suppl. 1 (2006), 61–65 | DOI
[13] N. B. Ayupova, V. P. Golubyatnikov, “On two classes of nonlinear dynamical systems: four-dimensional case”, Sib. Math. J., 56:2 (2015), 231–236 | DOI | MR | Zbl
[14] M. V. Kazantsev, “On some properties of the domain graph of dynamical systems”, Sib. Zh. Ind. Mat., 18:4 (2015), 42–49 (in Russian) | MR
[15] Yu. A. Gaidov, V. P. Golubyatnikov, “On some nonlinear dynamical systems which model asymmetric gene networks”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 7:2 (2007), 8–17 (in Russian)