Analysis and synthesis of oscillator systems described by perturbed double hump Duffing equations

This paper presents an analysis of oscillator systems described by double hump Duffing equations under polynomial perturbations of fourth degree. It has been proved that such a system can have unique hyperbolic limit cycle whose properties depend on the perturbation coefficients. The analytical condition for the arising of a limit cycle has been derived. Moreover, a method for the synthesis of oscillator systems of the considered type, having preliminarily assigned properties, is proposed. The synthesis consists of an appropriate choice of the perturbation coefficients in such a way that the oscillator equation is to have in advance assigned limit cycle. Both the analysis and the synthesis are performed with the aid of the Melnikov function. Copyright © 2010 John Wiley & Sons, Ltd.