Parameter switching in a generalized Duffing system: Finding the stable attractors

TL;DR

This paper introduces a parameter-switching technique for the generalized Duffing system that efficiently finds stable attractors by averaging switched parameters, verified through numerical simulations and phase analysis.

Contribution

It proposes a simple, effective parameter-switching method to identify stable attractors in a generalized Duffing system, enhancing attractor detection techniques.

Findings

The method accurately finds stable attractors matching averaged parameter values.

Phase plots and Hausdorff distance confirm the method's precision.

Extensive simulations demonstrate the approach's robustness.

Abstract

This paper presents a simple periodic parameter-switching method which can find any stable limit cycle that can be numerically approximated in a generalized Duffing system. In this method, the initial value problem of the system is numerically integrated and the control parameter is switched periodically within a chosen set of parameter values. The resulted attractor matches with the attractor obtained by using the average of the switched values. The accurate match is verified by phase plots and Hausdorff distance measure in extensive simulations.