This work presents a general theoretical framework for dynamic stabilization in nonlinear systems driven by high-frequency, zero-mean parametric forcing. Using multiscale perturbation theory and averaging methods, we identify two broad classes of systems. In discrete and network-based systems, high-frequency forcing renormalizes local interactions via a Bessel-function dependence. In continuum field systems, the same mechanism generates effective ponderomotive stresses that oppose instability growth. Despite their differences, these mechanisms exhibit a common macroscopic behavior: a crossover from instability- or trapping-dominated dynamics to a dynamically stabilized regime under sufficiently strong high-frequency forcing. The framework provides a unifying perspective across diverse domains, including quantum information, biophysics, active matter, fluid dynamics, plasma physics, and electrochemical systems. This work identifies a robust and transferable class of dynamic stabilization mechanisms applicable to a wide range of nonlinear systems.
Claudia Attaianese (Mon,) studied this question.