On the dynamics of the Rayleigh-Duffing oscillator
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}
scientific article; zbMATH DE number 7030106
scientific article