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.
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
\Bibitem{KanKri20}
\by A.~N.~Kanatnikov, A.~P.~Krishchenko
\paper Qualitative Properties of a Duffing System with Polynomial Nonlinearity
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 308
\pages 197--209
\publ Steklov Math. Inst. RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4055}
\crossref{https://doi.org/10.4213/tm4055}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4101851}
\elib{https://elibrary.ru/item.asp?id=43293262}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2020
\vol 308
\pages 184--195
\crossref{https://doi.org/10.1134/S0081543820010149}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000535370800014}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85085311906}
Linking options:
https://www.mathnet.ru/eng/tm4055
https://doi.org/10.4213/tm4055
https://www.mathnet.ru/eng/tm/v308/p197
This publication is cited in the following 1 articles:
V. I. Serdyukov, N. A. Serdyukova, S. I. Shishkina, “Quasi-fractal models of system sustainability”, International conference of numerical analysis and applied mathematics ICNAAM 2021, AIP Conf. Proc., 2849, 2023, 200007
Citation in format AMSBIB
Contact us: