Analysis and synthesis of oscillator systems described by perturbed single well Duffing equations

Zhivko Dimitrov Georgiev (1)

1 Department of Theoretical Electrical Engineering

The paper presents an analysis as well as a synthesis of oscillator systems described by single well Duffing equations under polynomial perturbations of fourth degree. It is proved that such a system can have a unique hyperbolic limit cycle. An analytical condition has been obtained for the arising of a limit cycle and an equation giving the parameters of this limit cycle. There has been proposed a method for the synthesis of oscillator systems of the considered type, having preliminarily assigned properties. The synthesis consists of an appropriate choice of the perturbation coefficients in such a way that the oscillator equation should have a preliminary assigned limit cycle. Both the analysis and the synthesis are performed with the help of the Melnikov function.

Mots clés: Duffing equation; Duffing oscillators; Limit cycles; Melnikov function; Elliptic functions; Synthesis of oscillator systems

Zhivko Dimitrov Georgiev. Analysis and synthesis of oscillator systems described by perturbed single well Duffing equations. Nonlinear Dynamics, 2010, 62 (4), pp.883-893. ⟨10.1007/s11071-010-9771-x⟩. ⟨hal-00611663⟩