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NONLINEAR DYNAMICS OF ELECTRONIC SYSTEMS 2004 (NDES 2004) is the twelfth in a series of international specialist workshops on Nonlinear Dynamics of Electronics Systems, since 1993, when the first NDES workshop took place in Dresden. Since then, the NDES has steadily increased its impact in the scientific community, becoming a truly international event, the largest of its kind in Europe. In 2004, the workshop brought together specialists in engineering and applied sciences, in physics and geophysics and in mathematics, in order to provide an opportunity to meet in a low-cost informal setting to address new theoretical and practical results, novel analysis and design methods in nonlinear dynamic systems and circuits and to discuss open problems in nonlinear science in general. NDES2004 has been organized and hosted by the Centro de Geofísica de Évora (Centre of Geophysics of Évora) of the University of Évora, Portugal. Évora is, since 1986, a UNESCO World Heritage Site. This book of proceedings contains all accepted papers, distributed among the following subjects: Circuit systems, Chaos, Stability and Control, Nonlinear Time Series Analysis, Chaos in Earth Sciences, Econophysics and Econometrics, Biological Systems and Synchronization. We are very grateful to the following sponsors: Fundação Eugénio de Almeida, Fundação Calouste Gulbenkian, Fundação para a Ciência e a Tecnologia, Câmara Municipal de Évora, Banco Espírito Santo, CARMIM – Reguengos de Monsaraz and Universidade de Évora. We are also very grateful to the invited speakers for contributing to NDES2004 and for meeting our deadlines. We express our warm thanks to all the technicians that enthusiastically collaborated to make this event a pleasant reality; in particular we would like to mention the contribution of Luis Almas (University of Évora). Finally we also thank all participants for their contributions and for coming. We wish all a very productive and enjoyable stay in Évora! Évora, April 15, 2004 The Editors

We discuss the phase control technique consisting of an applied square pulsed periodic perturbation. We explore the effect of such perturbations to the different terms of the Duffing oscillator. We find that the effect depends sensitively on how the perturbation is applied, indeed, it is specially effective when it modulates the cubic and the linear term and uneffective when applied to the driving term. Our results highlight the highly nontrivial role of the phase when applying a second periodic perturbation to a chaotic system.

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms of a Duffing oscillator. Using a real-time analog indicator able to discriminate on-the-fly periodic behaviors from chaos, we reconstruct experimentally the phase versus perturbation strength stability areas when periodic perturbations are applied to different terms governing the oscillator. We verify the system to be more sensitive to perturbations applied to the quadratic term of the double-well Duffing oscillator and to the quartic term of the single-well Duffing oscillator.