High-Order Variational Calculation for the Frequency of Time-Periodic Solutions

TL;DR

This paper introduces a convergent variational perturbation method to accurately compute the frequency of time-periodic solutions in nonlinear dynamical systems, demonstrated through the Duffing oscillator.

Contribution

It presents a novel convergent variational perturbation approach for calculating frequencies in nonlinear systems, improving upon existing methods.

Findings

Effective for the Duffing oscillator

Provides accurate frequency estimates

Demonstrates convergence of the method

Abstract

We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.