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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 141–153 (Mi timm815)  
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.

Full text: PDF file (241 kB)
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English version:
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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\by O.~M.~Kiselev
\paper Oscillations near a~separatrix in the Duffing equation
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 2
\pages 141--153
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 281
\issue , suppl. 1
\pages 82--94
\crossref{https://doi.org/10.1134/S0081543813050088}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. A. Kalyakin, “Asymptotic analysis of the model of gyromagnetic autoresonance”, Comput. Math. Math. Phys., 57:2 (2017), 281–296  mathnet  crossref  crossref  isi  elib
    2. L. A. Kalyakin, “Adiabatic approximation for a Model of Cyclotron Motion”, Math. Notes, 101:5 (2017), 850–862  mathnet  crossref  crossref  mathscinet  isi  elib
    3. 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  mathnet  crossref  crossref  isi  elib
    4. L. A. Kalyakin, “Capture and holding of resonance far from equilibrium”, Ufa Math. J., 10:4 (2018), 64–76  mathnet  crossref  isi
    5. 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  mathnet
    		• Trudy Instituta Matematiki i Mekhaniki UrO RAN
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