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

Abstract

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.

12 pages, 3 figures

Cited by in corpus (4)

• On connections of the Liénard equation with some equations of Painlevé--Gambier type
• Number and Amplitude of Limit Cycles emerging from {\it Topologically Equivalent} Perturbed Centers
• The Limit Cycles of Lienard Equations in the Strongly Non-Linear Regime
• The homotopy analysis method and the Lienard equation