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Innovative Methodologies for Analysis and Design of Chaotic Circuits
FIRB - RBNE012NSW, 2003-2005

During the last few years, increasing attention has been paid to the study of chaotic circuits and systems. This can be mostly ascribed to the growth of possible application fields where they can be successfully employed to possibly improve performances of existing solutions. Notwithstanding the importance of the problem and although some encouraging results have been obtained in this direction, no systematic design procedure for chaotic circuit has been proposed yet.  Aim of the present research project is to, at least partially, fill this gap, by developing new and improving existent theoretical methodologies and numerical techniques for the analysis and design of chaotic circuits.  As far as the initial analysis phase is concerned, the goal is, on one hand, to develop techniques, based on harmonic balance or envelope following methods, to study the global dynamics and the bifurcation process in electronic circuits and oscillators. Additionally, we will develop a new methodology for the analytic or semi-analytic study of high-order statistical features of the processes generated by chaotic maps and systems.  As far as the design rules are concerned, the developed methodologies will be applied to determine the intervals of parameters deviation in continuous- and discrete-time circuits and oscillators so that they exhibit (or not exhibit) chaotic behavior. Additionally, they will be used to design discrete-time chaotic circuits with prescribed statistical features.  The first phase will be followed by a more application oriented one, whose aim is twofold. On one hand, a collection of software packages and plug-ins to be inserted in a circuit simulator to increase its for analyzing the global dynamics of (RF) circuits and oscillators and for testing, without introducing any approximation, their robustness with respect to 1/f noise sources.  Finally, we will implement a chaotic map, based on an innovative mixed/mode structure, characterized by an high data-rate and capable of generating processes with at least partially programmable statistical features.

The Project aim are:  Methods for the analysis of continuous-time chaotic circuits; Methods for the analysis of arrays of continuous-time chaotic circuits; Methods for the analytical characterization and design of chaotic maps with prescribed statistical features; Numerical methods for the characterization of circuits in the frequency domain; Numerical methods for characterizing arrays of circuits in the frequency domain; Numerical methods for time-domain characterization of circuits and oscillators; Integration of innovative numerical methods and noise sources in a circuit simulator; Implementation of discrete-time chaos generators with pre-assigned statistical properties.
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