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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 308, Pages 197–209
DOI: https://doi.org/10.4213/tm4055 (Mi tm4055) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Qualitative Properties of a Duffing System with Polynomial Nonlinearity

A. N. Kanatnikov, A. P. Krishchenko

Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005 Russia
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DOI: https://doi.org/10.4213/tm4055
Abstract: The paper is devoted to the qualitative analysis of a nonautonomous Duffing equation with nonlinearity in the form of a monomial of odd degree. For all values of the parameters, compact localizing sets containing all compact invariant sets of the system are constructed. The behavior of the trajectories of the system outside the localizing set is analyzed, and it is shown that the trajectories of the system obey one of four scenarios.
Funding agency Grant number
Russian Foundation for Basic Research 20-07-00294
18-07-00269
This work was supported by the Russian Foundation for Basic Research, project nos. 18-07-00269 and 20-07-00294.
Received: February 17, 2019
Revised: July 14, 2019
Accepted: November 4, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 308, Pages 184–195
DOI: https://doi.org/10.1134/S0081543820010149
Bibliographic databases:
Document Type: Article
UDC: 517.938
Language: Russian
Citation: A. N. Kanatnikov, A. P. Krishchenko, “Qualitative Properties of a Duffing System with Polynomial Nonlinearity”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 308, Steklov Math. Inst. RAS, Moscow, 2020, 197–209; Proc. Steklov Inst. Math., 308 (2020), 184–195
Citation in format AMSBIB
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\bookinfo Collected papers
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\vol 308
\pages 197--209
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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    • This publication is cited in the following 1 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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