Analysis and synthesis of perturbed Duffing oscillators

Abstract

AbstractAnalysis and synthesis of perturbed Duffing oscillators have been presented. The oscillations in such systems are regarded as limit cycles in perturbed Hamiltonian systems under polynomial perturbations of sixth degree and are analysed by using the Melnikov function. It has been proved that there exists a polynomial perturbation depending on the zeros of the Melnikov function so that the system considered can have either two simple limit cycles, or one limit cycle of multiplicity 2, or one simple limit cycle. A synthesis of such oscillators based on the Melnikov's theory has been proposed. Copyright © 2006 John Wiley & Sons, Ltd.