Circuits and systems for the synthesis of chaotic signals in engineering applications

In this chapter we discuss the problem of "chaos generation", namely efficient techniques for the design of circuits to be employed as generators of chaotic signals (or sample sequences) in engineering applications. As intelligent computing techniques exploiting chaotic dynamics take momentum, synthesisers of chaotic waveforms become important design primitives. Consequently, design approaches suitable for cost containment, high robustness, and low susceptibility to external interference need to be formalised. This topic is particularly significant since digital hardware can deliver dynamics matching the characteristics of chaotic models only in the short term, and truly chaotic behaviour needs analog subsystems, for which design efforts are higher. The chapter opens with a concise history of chaotic circuits. This illustrates how the focus has progressively shifted from mere demonstrators, to circuits and systems finally optimised for typical merit indexes of engineering applications. The move from initial, mostly speculative designs to a real confrontation with emerging applications marked a key point in the design of "chaos generators". On one hand it posed precise statistical requirements and on the other hand it let important implementation robustness issues emerge. In the central part of the chapter, after a quick comparison of continuous-time vs discrete-time chaotic models, the focus goes on the latter. A brief review of techniques for their electronic implementation is presented illustrating how significant advantages can be obtained by concentrating on those that enable an eefficient reuse of existing hardware. A discussion on how chaotic circuits can be derived from Analog to Digital Converter (ADC) architectures is presented. Some hints at how the proposed approach also presents side advantages such as a particularly good rejection of interference is also provided. In the last part of the chapter, the effectiveness of the proposed approach is proved by measurements made on real prototypes. This part is also the occasion to underline that not always applications require "true analog chaos" but that when they do, the ability to achieve it by building blocks ready available on most electronic systems can lead to a strategic advantage.