Parametric resonance of systems with time-varying dissipation

A prototype of a system with periodically time-varying dissipation is analyzed. It is found that parametric excitation can occur even if the average dissipation is positive, although it is necessary that the dissipation be negative (amplification) over part of the cycle. The pump amplitude threshold and unstable phase angle are found for the unstable region near ω1=2ω0. It is also shown that a periodic instability cannot be dynamically stabilized by periodically varying the dissipation