In this chapter, a current based VLSI degree-two chaos generator is presented. The generator is based upon two unstable oscillators with feedbacks to themselves. The stability of the system is realized via the use of binary hysteresis. The chaotic nature of the signals is guaranteed by the Li-Yorke theorem through the generation of the period-three return map. The initial conditions of the system are discussed and an approach to change them to the origin is proposed. The simulation results are presented finally.

10.1 Introduction

Synthesis of simple chaotic oscillators has been studied extensively due to interest in investigating nonlinear phenomena. The idea of using hysteresis for generating chaos was suggested by R ssler ^[1]. In recent years, a number of hysteresis chaos generators have been published ^[2], ^[3], and ^[4]

This chapter is an extension of former work ^[2]. The 2-D chaotic signals presented in this chapter are generated in current based instead of voltage mode in ^[2]. Chaos is generated in this case by creating two planes in which second-order linear but unstable pseudo-trajectories are formed. However, because of hysteresis in the system, the true trajectories jump between these pseudo-trajectories in...