Abstract:
Stability of the limit cycles of small amplitude resulting from the Andronov–Hopf bifurcation is studied in a system of ordinary differential equations which describes the behavior of a hypothetical gene regulatory network.
Citation:
E. P. Volokitin, S. A. Treskov, “The Andronov–Hopf bifurcation in a model of a hypothetical gene regulatory network”, Sib. Zh. Ind. Mat., 8:1 (2005), 30–40; J. Appl. Industr. Math., 1:1 (2007), 127–136
This publication is cited in the following 11 articles:
V. P. Golubyatnikov, “O needinstvennosti tsiklov v trekhmernykh modelyakh koltsevykh gennykh setei”, Chelyab. fiz.-matem. zhurn., 9:1 (2024), 23–34
N. B. Ayupova, V. P. Golubyatnikov, “On two classes of nonlinear dynamical systems: The four-dimensional case”, Siberian Math. J., 56:2 (2015), 231–236
V. P. Golubyatnikov, A. E. Kalenykh, “On structure of phase portraits of some nonlinear dynamical systems”, J. Math. Sci., 215:4 (2016), 475–483
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
V. P. Golubyatnikov, I. V. Golubyatnikov, “On multidimensional models of gene networks”, J. Appl. Industr. Math., 5:3 (2011), 343–347
V. P. Golubyatnikov, I. V. Golubyatnikov, V. A. Likhoshvai, “On the existence and stability of cycles in five-dimensional models of gene networks”, Num. Anal. Appl., 3:4 (2010), 329–335
V. P. Golubyatnikov, I. V. Golubyatnikov, “O periodicheskikh traektoriyakh nelineinykh dinamicheskikh sistem spetsialnogo vida”, Vestn. NGU. Ser. matem., mekh., inform., 10:3 (2010), 3–16
J. Appl. Industr. Math., 4:1 (2010), 43–47
Yu. A. Gaidov, V. P. Golubyatnikov, “O nekotorykh nelineinykh dinamicheskikh sistemakh, modeliruyuschikh nesimmetrichnye gennye seti”, Vestn. NGU. Ser. matem., mekh., inform., 7:2 (2007), 19–27
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