Chua's Circuit Implementations: Yesterday, Today And Tomorrow

by Luigi Fortuna, Mattia Frasca, Maria Gabriella Xibilia

Overview

Since the birth of the Chua circuit in 1983, a considerable number of fruitful, fascinating and relevant research topics have arisen. In honor of the 25th anniversary of the invention of Chua's circuit, this book presents the 25 years of research on the implementation of Chua's circuit, and also discusses future directions and emerging applications of recent results.The purpose of the book is to provide researchers, PhD students, and undergraduate students a research monograph containing both fundamentals on the topics and advanced results that have been recently obtained. With about 60 illustrations included in the book, it also shows the detailed schematics of several different implementations that can be easily reproduced with a low-cost experimental setup and PC-based measurement instrumentation.

Product Details

ISBN-13:	9789812839244
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	04/16/2009
Series:	World Scientific Series On Nonlinear Science Series A , #65
Pages:	224
Product dimensions:	6.10(w) x 9.00(h) x 0.80(d)

Table of Contents

Preface vii

1 The birth of the Chua's circuit 1

1.1 Introduction 1

1.2 Genesis of the Chua's circuit 6

1.3 From RLC to Chua's equations 10

1.4 Dimensionless Chua's equations 14

1.5 Geometry of the double scroll 15

1.5.1 Parameter values for the Double Scroll Chua's Attractor 15

1.5.2 Equilibrium points of the Chua's circuit 16

1.5.3 Stability of the equilibrium points 17

1.5.4 General considerations on the behavior on each of the three regions D1, Do and D-1 18

1.5.5 Qualitative description of the dynamics in D1 (or D-1) 19

1.5.6 Qualitative description of the dynamics in D0 20

1.5.7 The double scroll attractor 20

1.5.8 Rigorous proof of chaos in the Chua's circuit 21

1.6 Bifurcations of the Chua's circuit 23

1.7 The Chua's oscillator 27

1.8 Generalizations of the Chua's Circuit 38

1.8.1 Sinusoidal forcing in the Chua's circuit 38

1.8.2 Hyperchaos in the Chua's circuit 40

1.8.3 The Chua's circuit with a smooth nonlinearity 42

1.8.4 The n-scroll chaotic attractor 43

1.9 Control of the Chua's circuit 44

1.10 Synchronization of Chua's circuits 51

2 Implementation of the Chua's diode 61

2.1 Circuits based on operational amplifiers 61

2.2 Implementation of a negative resistance 66

2.3 Implementation of the five segment nonlinearity 68

2.4 Implementation of the NR characteristic with diodes 69

2.5 Two implementations of the Chua's circuit 71

2.6 Other implementations of the Chua's diode 74

3 Cellular Nonlinear Networks and Chua's circuit 77

3.1 Brief overview on CNN architectures 77

3.2 The State Controlled Cellular Nonlinear Network 80

3.3 CNN-based implementation of the Chua's circuit 80

3.4 Improved cell realization forSC-CNN based Chua's circuit 82

3.5 SC-CNN-based implementation of the Chua's oscillator 86

4 Frequency switched Chua's circuit: experimental dynamics characterization 91

4.1 Model 91

4.2 Experimental results 93

5 Photo-controlled Chua's circuit 101

5.1 The nonlinear photo-controlled device 101

5.2 The photo-controlled Chua's circuit 103

5.3 Experimental results 104

6 Programmable Chua's circuit 113

6.1 The Development System 114

6.2 Anadigm Software Development Tool 115

6.3 Design of the Chua's circuit 116

6.4 Circuit implementation and experimental results 117

7 Switched capacitor-based Chua's circuit 125

7.1 Design of the switched capacitor Chua's circuit 126

7.2 Simulation results and layout of the circuit 129

7.3 Experimental results 130

7.4 A cell to experimentally characterize discretely-coupled Chua's circuits 131

8 The four-element Chua's circuit 137

8.1 Model 137

8.2 Implementation 141

8.3 Chua's circuit and the memristor 143

9 The organic Chua's circuit 145

9.1 The OTFT device 146

9.2 Implementation of the Organic Chua's Circuit 148

9.2.1 Saturation Block 150

9.2.2 Transconductance Amplifier Block 151

9.2.3 Negative Current Block 152

9.3 Experimental Results 153

10 Applications of the Chua's circuit 159

10.1 Chaos does help motion control 160

10.1.1 Motion control 161

10.1.2 Experimental results 164

10.2 The Chua's circuit as an analog noise generator 167

10.3 Chaotic Pulse Position Modulation to improve the efficiency of Sonar Sensors 167

10.3.1 Continuous Chaotic Pulse Position Modulation 169

10.3.2 The CPPM Sonar 172

10.3.3 Experimental results 173

11 Conclusions 179

11.1 Scheme of the book 181

Critical bibliography 183

Bibliography 193

Index of the implementations 207

Index 209