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This article is cited in 5 scientific papers (total in 5 papers)
Oscillations near a separatrix in the Duffing equation
O. M. Kiselev Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Abstract:
A small periodic perturbation results in a complicated dynamics near separatrices and saddle points. A two-parameter family of asymptotic solutions staying near separatrices for a long time is constructed. Solutions from this family depend nonsmoothly on the disturbance parameter. An example is given in which the values of the disturbance parameter for this family of solutions are determined by a set with structure of the type of the Cantor set.
Keywords:
perturbation, separatrix, oscillations.
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Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 281, suppl. 1, 82–94
Bibliographic databases:
UDC:
517.977 Received: 01.10.2011
Citation:
O. M. Kiselev, “Oscillations near a separatrix in the Duffing equation”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 141–153; Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 82–94
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/timm815 http://mi.mathnet.ru/eng/timm/v18/i2/p141
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L. A. Kalyakin, “Adiabatic approximation for a Model of Cyclotron Motion”, Math. Notes, 101:5 (2017), 850–862
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O. M. Kiselev, V. Yu. Novokshenov, “Autoresonance in a model of a terahertz wave generator”, Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 88–102
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L. A. Kalyakin, “Capture and holding of resonance far from equilibrium”, Ufa Math. J., 10:4 (2018), 64–76
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O. M. Kiselev, “Ravnomernaya asimptotika funktsii sinus amplitudy”, Differentsialnye uravneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 163, VINITI RAN, M., 2019, 25–38
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