We revisit the mean field model of globally and harmonically coupled parametric oscillators subject to periodic block pulses with initially random phases. The phase diagram of regions of collective parametric instability is presented, as is a detailed characterization of the motions underlying these instabilities. This presentation includes regimes not identified in earlier work [I. Bena and C....

We gain new fundamental insights on parametric instabilities that are at the heart of many physical phenomena from dynamic buckling slender structures in periodic compression to emergence Faraday waves or spontaneous symmetry breaking Floquet time crystals. Combining theoretical models and precision desktop experiments, we explain how periodically vary evolution function a dynamical system enha...

Parametric instabilities driven by partially coherent radiation in plasmas are described by a generalized statistical Wigner-Moyal set of equations, formally equivalent to the full wave equation, coupled to the plasma fluid equations. A generalized dispersion relation for stimulated Raman scattering driven by a partially coherent pump field is derived, revealing a growth rate dependence, with t...