Branch inclusion in generic Hopf bifurcation: The case of scaled van der Pol's equation (Q1181074)

The limit cycles of an ordinary second order differential equation in the vicinity of a Hopf bifurcation point are calculated by averaging and a rescaling method. The Newton-Kantorovich theorem yields error estimates for the corresponding asymptotic expansions of the amplitude and the period. The calculations are carried out for a scaled version of van der Pol's equation with cubic nonlinearities, yielding good estimates to quadratic order.