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Variational approach to a class of nonlinear oscillators with several limit cycles

M. C. Depassier·J. Mura
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Abstract

We study limit cycles of nonlinear oscillators described by the equation $\ddot x + νF(\dot x) + x =0$. 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 $ν->0$ and $ν-> \infty$ are in agreement with previously known criteria. For intermediate $ν$ numerical determination of the limit cycles can be obtained.

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M. C. Depassier, J. Mura. 2001-03-22. Variational approach to a class of nonlinear oscillators with several limit cycles. https://doi.org/10.1103/physreve.64.056217

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