# Capture into parametric autoresonance in the presence of noise

## TL;DR

This paper investigates the stability of systems entering parametric autoresonance under white noise perturbations, demonstrating conditions where capture remains highly probable despite persistent noise influences.

## Contribution

It introduces a stability analysis of autoresonant solutions under white noise, showing that capture can be maintained with high probability under specific noise conditions.

## Key findings

- Capture into autoresonance persists with high probability under certain noise intensities.
- Stability of autoresonant solutions is analyzed with respect to white noise perturbations.
- Conditions for noise levels that preserve autoresonance are identified.

## Abstract

System of differential equations describing the initial stage of the capture of oscillatory systems into the parametric autoresonance is considered. Of special interest are solutions whose amplitude increases without bound with time. The possibility of capture the system into the autoresonance is related with the stability of such solutions. We study the stability of autoresonant solutions with respect to persistent perturbations of white noise type, and we show that under certain conditions on the intensity of the noise, the capture into parametric autoresonance is preserved with probability tending to one.