Formal asymptotics of parametric subresonance

TL;DR

This paper derives asymptotic formulas for parametric subresonance, including the growth of oscillation amplitude and the transition point to bounded oscillations, validated by numerical comparison.

Contribution

It provides a new asymptotic analysis of parametric subresonance, including explicit formulas for growth and transition times.

Findings

Asymptotic formulas for amplitude growth were derived.

The transition time from growth to bounded oscillations was explicitly calculated.

Numerical results confirmed the accuracy of the asymptotic approximations.

Abstract

The system of equations for parametric sub-resonant growth of the amplitude of oscillations was obtained. The time of turning point from the growing of the amplitude to the bounded oscillations in the slow variable was found. The comparison between the asymptotic approximation for the turning time and numerical one is shown.