Bifurcations of Parametrically Forced Oscillators

摘要

A parametrically forced oscillator, i.e. an oscillator with periodically varyingcoefficients, near resonance, is addressed. There exists a vast amount of literature on this subject, especially on the linear case which involves differential equations of Mathieu type. The nonlinear problem, localized near a central equilibrium solution of the free oscillator, is addressed. In particular, the branching off of certain subharmonic periodic solutions is studied, and more general bifurcational aspects of this.