Random Perturbations of a Periodically Driven Nonlinear Oscillator: Escape from a resonance zone

TL;DR

This paper investigates how weak noise influences the escape dynamics of a nonlinear oscillator from resonance zones under periodic driving, extending understanding of stochastic effects in nonlinear systems.

Contribution

It introduces an analysis of noise-induced escape from resonance zones in a periodically driven nonlinear oscillator, a problem not fully addressed in prior deterministic studies.

Findings

Weak noise facilitates escape from resonance zones.

The measure of initial conditions leading to capture decreases with noise.

Results provide insights into stochastic resonance phenomena.

Abstract

The phase space for a periodically driven nonlinear oscillator consists of many resonance zones. Let the strength of periodic excitation and the strength of the damping be indexed by a small parameter $\varepsilon$. It is well known that, as $\varepsilon \to 0$, the measure of the set of initial conditions which lead to 'capture in a resonance zone' goes to zero. In this paper we study the effect of weak noise on the escape from a resonance zone.