Preface

This book introduces novel concepts of various areas of physics, computer and electrical engineering. For instance, we present a synthesis methodology to design multi-scrolls chaotic oscillators by dividing the process into three hierarchical levels of abstraction. The first one is the electronic system level, supported by performing high-level behavioural modelling and simulation, and allows exploring a wide range of parameters for the generation of multi-scrolls chaos generators. At this level, to speed-up time simulation, we implement a procedure for the automatic control and determination of step-size in multi-step algorithms. The second level is devoted to use behavioural models of the electronics devices within Verilog-A to describe the hardware of the nonlinear dynamical system. Computer and electrical experts coexist at this level because we show the synthesis of the mathematical descriptions by a block diagram which takes into account the real behaviour of electronic devices. The excursion levels of the chaotic signals are scaled within values that can be synthesized using behavioural models to control the breaking points and slopes of saturated functions. The third level of the Electronic Design Automation (EDA) approach is the selection of an electronic device to implement the chaotic generator. A good repertoire of multi-scrolls chaos generators is presented by dealing with one-dimensional (1D), 2D and 3D oscillators, which respectively requires one, two or three piecewise-linear (PWL) functions. We show the design of the PWL functions by using operational amplifiers (opamps). However, since the high-level approach uses behavioural models, other novel analog integrated circuits (ICs) can be used to implement the chaos generators. To highlight the usefulness of the designed multi-scrolls chaotic oscillators, we present the realization of a secure communication system. Although this application uses commercially available opamps, this is an important part of the book since it opens new lines for future EDA and IC design research, while providing a tutorial for educational purposes.