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A series resonance circuit that consists of a linear inductance, a nonlinear capacitance and a sinusoidal driving is investigated. The nonlinearity arises from a ferroelectric crystal. We observed the Feigenbaum scenario, crises, periodic windows inside chaos that show a period adding behaviour and coexisting attractors of different symmetry. We conclude a Duffing equation to cover all significant properties of our dynamical system.

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A series resonance circuit under sinuousoidal driving is investigated experimentally. The inductance consists of an air coil. The capacitance is made up of a ferroelectric material that introduces its nonlinear dielectric properties into the circuit. The dynamical system linear coil -nonlinear capacaitor shows an interesting behaviour. The phase portrait differs in general from the ellipse of the harmonic oscillator. For appropriate external conditions period doubling sequences, chaos and therein enclosed periodic windows might occur. Starting from a cubic nonlinearity of the dielectric properties a Duffing equation is proposed as a model for periodic behaviour of the series resonance circuit. Simulations of experimentally recorded phase portraits yield good agreement between experiment and model.

Ferroelectric materials are rather exactly specified for small signal application by their linear elastic, dielectric and electromechanical coefficients. However, an unambigeous characterization cannot be given by these means if a high mechanical or electrical power level is applied. Further the study of the large signal behaviour is important for the understanding of structural phase transitions of ferroelectric materials (ceramics, crystals and thin films). The aim of the present paper is to show that the application of methods of nonlinear dynamics, e.g. spectrum-and time series analysis, is a useful tool for studying this large signal behaviour . Investigations concerning the nonlinear behaviour of ferroelectric materials were performed in a wide range of parameters of a driven series resonance circuit. The bifurcation cascades, the periodic and chaotic phase portraits and the Poincar6 sections were used for the determination of the nonlinear coefficients of the sample.