A perturbation method for the analysis of vibrations and bifurcations associated with non-autonomous systems. I: Non-resonance case (Q1187553)

A new perturbation technique, based on the intrinsic harmonic balancing and time scaling, is developed for the analysis of vibration and bifurcation problems associated with non-autonomous systems. The application of the technique to specific problems is illustrated on several examples. In particular, the problem of perturbed Hopf bifurcations arising in non-autonomous systems is analysed in general terms such that the results are applicable to all specific problems within the scope of the general formulation.