In differential equations, parametric excitation refers to situations where a parameter which is usually kept constant is instead forced to vary sinusoidally in time. Take for example the simple harmonic oscillator whose frequency parameter w is normally constant. Parametric excitation occurs if w is forced to vary sinusoidally in time. In this case, there is a resonance between the forcing frequency and the unforced frequency of the oscillator. The largest instability corresponds to 2:1 resonance.

In this seminar I will review classic parametric excitation, and describe a new form based on differential-delay equations (DDE). In work with Lauren Lazarus and Matthew Davidow, we have discovered that 2:1 parametric resonance can occur if the delay, normally kept constant, is forced to vary sinusoidally in time. Here the frequency of the delay lies in the neighborhood of twice the frequency of the limit cycle occurring in the DDE.