# Stabilization of unstable autoresonant modes

## TL;DR

This paper investigates how slowly decreasing parametric perturbations can stabilize unstable autoresonant modes in oscillatory systems, ensuring physically observable solutions.

## Contribution

It introduces a method of stabilizing unstable autoresonant solutions using adiabatically varying parametric perturbations with decreasing amplitude.

## Key findings

- Decreasing amplitude perturbations can stabilize unstable autoresonant modes.
- Stable solutions correspond to physically observable motions.
- The approach enhances control over autoresonant systems.

## Abstract

A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the autoresonance phenomenon. Stability of such solutions is of great importance because only stable solutions correspond to physically observable motions. We study the stabilizing problem and we show that the adiabatically varying parametric perturbation with decreasing amplitude in time can stabilize the unstable autoresonant modes.