On the dynamics of the Rayleigh-Duffing oscillator
type: Item
instance of: scholarly article
title: On the dynamics of the Rayleigh-Duffing oscillator
zbMATH Open document ID: 1415.34059
author: Jaume Giné
author: Claudia Valls
published in: Nonlinear Analysis. Real World Applications
publication date: 2019-02-27T00:00:00Z
review text: Consider the planar system \[ \frac{dx}{dt}= y,\quad \frac{dy}{dt}=-ax-2bxy-x^3-y^3. \] The authors prove that this system \begin{itemize} \item[(i)] has no global analytic first integrals, \item[(ii)] has no Darboux polynomials, \item[(iii)] is not Darboux integrable, \item[(iv)] is not Liouville integrable, \item[(v)] does not have any center neither nondegenerate nor nilpotent. \end{itemize}
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 7030106
zbMATH Keywords: Rayleigh-Duffing oscillator
zbMATH Keywords: first integrals
zbMATH Keywords: center problem
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2018.07.007
OpenAlex ID: W2883925788
cites work: Global study of Rayleigh–Duffing oscillators
cites work: Creation-annihilation process of limit cycles in the Rayleigh-Duffing oscillator
cites work: Q5310344
cites work: Essential variables in the integrability problem of planar vector fields
cites work: On some open problems in planar differential systems and Hilbert's 16th problem
cites work: Qualitative theory of planar differential systems
cites work: Liouvillian First Integrals of Differential Equations
cites work: On the differentiability of first integrals of two dimensional flows
cites work: The Bianchi VIII model is neither global analytic nor Darboux integrable
Wikidata QID: Q129482011
DOI: 10.1016/J.NONRWA.2018.07.007
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description: scientific article; zbMATH DE number 7030106