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Trudy Instituta Matematiki i Mekhaniki 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
Full-text PDF (241 kB) Citations (5)
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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.
Received: 01.10.2011
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, Volume 281, Issue 1, Pages 82–94
DOI: https://doi.org/10.1134/S0081543813050088
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
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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\paper Oscillations near a~separatrix in the Duffing equation
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\pages 141--153
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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