Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations

摘要

A method for the analysis of perturbations of integrable planar systems of differential equations is developed. Concentrating on the case in which the unperturbed system is Hamiltonian and the perturbation introduces dissipation and time-periodic forcing, the global solution curves of the unperturbed system are used in regular perturbation calculations to locate subharmonic orbits and homoclinic orbits and to characterize the bifurcations in which they are created as external parameters are varied. The results are applied to Duffing's equation and applications to the chaotic motions of buckled elastic beams undergoing periodic excitation are given. (Author)