Variational approach to a class of nonlinear oscillators with several limit cycles - art. no. 056217

We study limit cycles of nonlinear oscillators described by the equation (x )double over dot + vF(x)over dot + x = 0 with F an odd function. Depending on the nonlinearity, this equation may exhibit one or more limit cycles. We show that limit cycles cot-respond to relative extrema of a certain functi onal. Analytical results in the limits v -->0 and v --> infinity are in agr eement with previously known criteria. For intermediate v, numerical determ ination of the limit cycles can be obtained.