A perturbation-incremental method for strongly non-linear non-autonomous oscillators

A perturbation-incremental method is extended for the analysis of strongly non-linear non-autonomous oscillators of the form x¨+g(x)=εf(x,x˙,Ωt), where g(x) and f(x,x˙,Ωt) are arbitrary non-linear functions of their arguments, and ε can take arbitrary values. Limit cycles of the oscillators can be calculated to any desired degree of accuracy and their stabilities are determined by the Floquet theory. Branch switching at period-doubling bifurcation along a frequency-response curve is made simple by the present method. Subsequent continuation of an emanating branch is also discussed.