ISBN: 3-540-65202-7
TITLE: Cellular Neural Networks
AUTHOR: Manganaro, Gabriele; Arena, Paolo; Fortuna, Luigi
TOC:

Part I. Circuit Theory and Applications of CNNs
1. CNN Basics 3
1.1 The CNN of Chua and Yang 3
1.1.1 The Cell 4
1.1.2 The CNN Array 5
1.1.3 More About Templates 7
1.1.4 Multilayer CNNs 9
1.1.5 The CNN as an Analog Processor 10
1.1.6 Some Stability Results 11
1.2 Main Generalizations 15
1.2.1 Nonlinear CNNs and Delay CNNs 15
1.2.2 Nonuniform Processor CNNs and Multiple Neighborhood Size CNNs 17
1.2.3 Discrete-Time CNNs 17
1.2.4 The CNN Universal Machine 19
1.3 A Formal Definition 20
1.3.1 The Cells and Their Coupling 20
1.3.2 Boundary Conditions 22
1.4 Summary 23
2. Some Applications of CNNs 25
2.1 CNN-Based Image Pre-processing for the Automatic Classification of Fruits 25
2.1.1 The Pre-filtering 26
2.2 Processing of NMR Spectra 28
2.2.1 Two-Dimensional NMR Spectra 29
2.2.2 Processing of NMR Spectra with CNNs 30
2.2.3 Description of the Dual Algorithm 32
2.3 Air Quality Modeling 35
2.3.1 Models 35
2.3.2 CNNs for Air Quality Modeling 36
2.3.3 Examples 39
2.4 Conclusions 40
3. The CNN as a Generator of Nonlinear Dynamics 43
3.1 The State Controlled CNN Model 44
3.1.1 Discrete Components Realization of SC-CNN Cells 45
3.2 Chua Oscillator Dynamics Generated by the SC-CNN 47
3.2.1 Main Result 47
3.2.2 Experimental Results 49
3.3 Chaotic Dynamics of a Colpitts Oscillator 51
3.4 Hysteresis Hyperchaotic Oscillator 55
3.5 n-Double Scroll Attractors 58
3.5.1 A New Realization of the n-Double Scroll Family 58
3.5.2 n-Double Scrolls in SC-CNNs 65
3.6 Nonlinear Dynamics Potpourri 66
3.6.1 A Non-autonomous Second Order Chaotic Circuit 66
3.6.2 A Circuit with a Nonlinear Reactive Element 68
3.6.3 Canards and Chaos 70
3.6.4 Multimode Chaos in Coupled Oscillators 72
3.6.5 Coupled Circuits 74
3.7 General Case and Conclusions75
3.7.1 Theoretical Implications 77
3.7.2 Practical Implications 77
4. Synchronization 79
4.1 Background 79
4.1.1 PecoraCarroll Approach 80
4.1.2 Inverse System Approach 81
4.2 Experimental Signal Transmission Using Synchronized SC-CNN 81
4.2.1 Circuit Description 82
4.2.2 Synchronization: Results of Experiment and Simulation 83
4.2.3 Non-ideal Channel Effects 86
4.2.4 Effects of Additive Noise and Disturbances on the Channel 87
4.3 Chaotic System Identification 93
4.3.1 Description of the Algorithm 93
4.3.2 Identification of the Chua Oscillator 95
4.3.3 Examples 96
4.4 Summary and Conclusions 101
5. Spatio-temporal Phenomena 105
5.1 Analysis of the Cell 105
5.1.1 Fixed Points 107
5.1.2 Limit Cycle and Bifurcations 109
5.1.3 SlowFast Dynamics 110
5.1.4 Some Simulation Results 112
5.2 The Two-Layer CNN 112
5.3 Traveling Wavefronts 115
5.3.1 Autowaves 116
5.3.2 Labyrinths 118
5.4 Pattern Formation 120
5.4.1 Condition for the Existence of Turing Patterns in Arrays of Coupled Circuits 121
5.4.2 Turing Patterns in the Two-Layer CNN 122
5.4.3 Simulation Results 124
5.5 Sensitivity to Parametric Uncertainties and Noise 127
5.5.1 Spiral Wave: Parametric Uncertainty 127
5.5.2 Spiral Waves: Presence of Noise in the Initial Conditions 129
5.5.3 Patterns: Parametric Uncertainties 130
5.6 Summary and Conclusions 132
6. Experimental CNN Setup and Applications to Motion Control 133
6.1 The Experimental Setup 134
6.1.1 Realization of the Cell for Autowave Generation 135
6.1.2 Realization of the Cell for Pattern formation 136
6.1.3 Realization of the Laplacian Couplings and Boundary Conditions 138
6.1.4 Realization of the Main Board 139
6.1.5 Autowave Experiments 140
6.2 Pattern Formation and Propagation 142
6.3 CNNs for Generating and Controlling Artificial Locomotion 149
6.3.1 Links to Biological Locomotion 149
6.3.2 WORMBOT: A Ring-Worm-like Walking Robot 152
6.3.3 REXABOT: An Hexapode ReactionDiffusion Walking Robot 154
6.3.4 READIBELT: Reaction Diffusion Conveyor Belt Autowave Driven 159
6.4 Conclusion 160
Part II. Implementation and Design
7. A Four Quadrant S^2I Switched-Current Multiplier 167
7.1 Detailed Analysis of the S^2I Memory Cell 168
7.2 The Multiplier Architecture 173
7.3 Analysis and Design of the S^2I Multiplier 177
7.3.1 Circuit Analysis of the Multiplier 177
7.3.2 Circuit Design 180
7.4 Experimental Performance Evaluation 182
7.5 Summary 186
8. A One-Dimensional Discrete-Time CNN Chip for Audio Signal Processing. 189
8.1 System Architecture 189
8.2 The Tapped Delay Line 190
8.3 CNN Cells 192
8.3.1 Multiplier and Ancillary Circuitry 193
8.4 Cell Behavior and Hardware Multiplexing 197
8.5 Results and Example 199
8.6 Summary 203
A. Mathematical Background 205
A.1 Topology 205
A.2 Operations and Functions 206
A.3 Matrices 207
A.4 Dimension 207
A.5 Dynamical Systems: Basic Definitions 208
A.6 Steady-State Behavior 209
A.6.1 Classification of Asymptotic Behavior 210
A.7 Stability 212
A.7.1 Stability of equilibrium points 212
A.7.2 Stability of Limit Cycles 217
A.7.3 Lyapunov Exponents 219
A.8 Topological Equivalence and Conjugacy, Structural Stability and Bifurcations 220
A.9 Silnikov Method 221
A.10 Particular Results for Two-Dimensional Flows 222
B. Library of Templates 225
References 259
Index 271
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