Threshold values of autoresonant pumping

TL;DR

This paper analyzes the conditions under which stable autoresonant solutions grow with decreasing pumping amplitude, identifying the amplitude interval that sustains such solutions and characterizing their asymptotic behavior.

Contribution

It determines the amplitude interval for autoresonant pumping that allows stable growth and derives the primary asymptotic term independent of force order.

Findings

Stable growing solutions exist for specific amplitude intervals.

The primary asymptotic term is proportional to (\u221a{t}) and independent of force order.

The amplitude interval for stable solutions is explicitly characterized.

Abstract

There exists stable growing solution of primary resonant equation for a autoresonant pumping with decreasing amplitude. The primary term of asymptotics is $O(\sqrt{t})$ and does not depend on order of the force from some interval. We point to the interval for the amplitude of the pumping for which the growing stable solution exists.