Preface

Chaos is an ubiquitous phenomenon that arises in many natural and artificial systems where nonlinearity is present (Thompson & Stewart 1986; Moon 1992). Nowhere is this important and robust phenomenon more easily observed, studied and exploited than in electronic circuits. Three reasons for this can be identified. First, there exist exceedingly simple and inexpensive circuits costing less than a paperback, which are ideal for heuristic experimental investigations of the diverse chaotic phenomena that have been identified in the more complex systems of solid and fluid dynamics, chemical kinetics, etc. Second, the physics of the electronic devices used in these circuits is a well-understood and mature branch of electrical engineering. Excellent mathematical models exist, allowing the experimental observations to be reproduced by computer simulation (Parker & Chua 1989) with great accuracy; and the bifurcational structure of these nonlinear models can be analysed by using the new topological techniques of dynamical systems theory. It is indeed the case that no other chaotic physical systems are known which are amenable simultaneously to experimental, numerical and analytical studies, giving correlations which are not only qualitative but often quantitative to within 5%. Third, for applications which call for a source of real chaotic signals (such as secure communication systems and neural networks), electronic circuits provide the simplest and cheapest source of such physical signals. Moreover, such circuits can be readily mass-produced in practical applications as inexpensive integrated circuit chips