Stroboscopic averaging methods to study autoresonance and other problems with slowly varying forcing frequencies

TL;DR

This paper develops a modified stroboscopic averaging method to effectively analyze autoresonance phenomena in nonlinear oscillators with slowly varying forcing frequencies, demonstrating computational efficiency through numerical experiments.

Contribution

The paper introduces a modification to the stroboscopic averaging method to handle slowly varying forcing frequencies in autoresonance studies.

Findings

Modified SAM effectively captures autoresonance dynamics.

Numerical experiments show computational efficiency gains.

Method applicable to other slowly varying oscillatory systems.

Abstract

Autoresonance is a phenomenon of physical interest that may take place when a nonlinear oscillator is forced at a frequency that varies slowly. The stroboscopic averaging method (SAM), which provides an efficient numerical technique for the integration of highly oscillatory systems, cannot be used directly to study autoresonance due to the slow changes of the forcing frequency. We study how to modify SAM to cater for such slow variations. Numerical experiments show the computational advantages of using SAM.