Emergence of stability in a stochastically driven pendulum: beyond the Kapitsa effect

TL;DR

This paper demonstrates that a nonlinear pendulum can be stabilized by multiplicative noise in a regime where traditional Kapitsa effects do not apply, revealing a novel noise-induced stabilization mechanism.

Contribution

It shows that stochastic stabilization can occur beyond the classical Kapitsa effect, especially in strong-noise regimes where WKB approximation fails.

Findings

Upper equilibrium point stabilization by white noise

Stabilization occurs outside the Kapitsa effect regime

Strong-noise regime where WKB approximation is invalid

Abstract

We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped non-linear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that the upper equilibrium point of the pendulum can become stable even when the noise is white, and the "Kapitsa pendulum" effect is not at work. The stabilization occurs in a strong-noise regime where WKB approximation does not hold.