On a new criterion for evaluating the stability of the limit cycles of perturbed duffing oscillators

Abstract

A criterion for finding the orbital asymptotic stability of the limit cycles of the perturbed Duffing oscillators , based on a method of Krylov–BogoHubov type that uses Jacobi elliptic functions in the approximate solution, is shown to be equivalent to a current well-known criterion, sometimes called the Poincarè criterion. As an example, both criteria are applied to the Duffing oscillator perturbed with the van der Pol term