Parametric excitation of multimode dissipative systems

A general approach to the study of parametric excitation of multimode dissipative systems is proposed. It is based on the derivation of normal form equations and on the reduction of these equations to flow of lower dimensionality. General results for single- and double-mode systems are presented. The implications for the system of parametrically excited surface waves are discussed; it is predicted that the onset of waves can be either smooth or hysteretic depending on the excitation frequency, and an explanation is given for the experimentally observed mode-suppression effect, occurring in double-mode systems.