In this chapter, we introduce a four-dimensional chaotic oscillator based on two-port voltage-controlled current sources (named 2PVCCSs). The circuit consists of one-linear 2PVCCS, one binary hysteresis 2PVCCS, and two capacitors. The hysteresis 2PVCCS has two jumps that correspond to the third and fourth states apart from the two capacitor voltages. The circuit exhibits double-screw chaotic attractors, quad-screw chaotic attractors, and related periodic attractors. Since the circuit is piecewise linear, the dynamics can be analyzed using the exact piecewise solution. A basic condition for the existence of attractors is given. A transistorized implementation is also presented with some typical SPICE simulations.

7.1 Introduction

Synthesis of simple chaotic oscillators has been extensively studied ^[1]- ^[16], at least for two reasons: First, such oscillators are useful tools for investigation of interesting nonlinear phenomena: chaos, synchronization, bifurcation, and so on. Second, such oscillators may be further developed for new engineering applications: dynamic associative memories, chaos-based multiplex communications, EMC improvement in DC/DC converters, and so on (see ^{[18] , [20]} and references therein).

In the last two decades, tremendous work pertaining to various chaotic oscillators have been published, for instance, Chua's circuit family ^{[1] [6]}, variations of classical oscillators ^{[7] , [8]}, hysteresis and switched chaotic oscillators ^{[9] [16]}, chaotic cellular neural networks ^[17],...