%0 Journal Article
%T Variational approach to a class of nonlinear oscillators with several limit cycles
%A M. C. Depassier
%A J. Mura
%J Physics
%D 2001
%I arXiv
%R 10.1103/PhysRevE.64.056217
%X We study limit cycles of nonlinear oscillators described by the equation $\ddot x + \nu F(\dot x) + x =0$. Depending on the nonlinearity this equation may exhibit different number of limit cycles. We show that limit cycles correspond to relative extrema of a certain functional. Analytical results in the limits $\nu ->0$ and $\nu -> \infty$ are in agreement with previously known criteria. For intermediate $\nu$ numerical determination of the limit cycles can be obtained.
%U http://arxiv.org/abs/nlin/0103034v1