Chapter 9: Some New Circuit Design for Chaos Generation

This chapter discusses some new circuitry design of chaos generation in simple three-dimensional autonomous systems. The well-known Chua's circuit will be adopted as the framework for basic design. We aim at designing some simple circuits to realize distinct nonlinearities, including smooth nonlinear functions and piecewise-linear functions of one variable, to purposely create chaos. The main theme of the chapter is three-fold. First, we introduce some techniques for chaos generation using smooth nonlinear functions, where a new family of smooth continuous nonlinear functions that can generate multi-scroll attractors is proposed. Second, we present some simple chaos generating circuits by using a piecewise-quadratic function, x x, and a piecewise-linear function, respectively, where attractors with multi-scrolls can be easily obtained by adding break points in the piecewise-linear function. Finally, a circuit design for realizing Chen's chaotic attractor, generated by simple smooth quadratic functions, is suggested. The chapter thus presents several snapshots on simple circuitry design for chaos generation.

9.1 Introduction

It has been gradually recognized that chaos can be quite useful in some novel time- and/or energy-critical applications, and there is some growing interest in utilizing the very nature of chaos, particularly for some nontraditional engineering and technological applications ^[1]. The main reason is that the complex chaos, when under control, can provide a system designer with a...