Variational approach to a class of nonlinear oscillators with several limit cycles
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.
nlin.CD↗