Cellular Neural Networks : Chaos, Complexity and VLSI Processing

by Manganaro, G.; Arena, Paolo; Fortuna, L.; Manganaro, G.; Arena, Paolo; Fortuna, L.

• ISBN13: 9783540652021
• ISBN10: 3540652027
• Format: Hardcover
• Copyright: 1999-05-01
• Publisher: Springer Verlag

Summary

Discusses new applications of cellular neural networks (CNNs), new theoretical results and implementation issues. Involves several scientific disciplines including circuit theory, microelectronics, and information processing. DLC: Neural networks (Computer science).

Table of Contents

Part I. Circuit Theory and Applications of CNNs
CNN Basics	3	(22)
The CNN of Chua and Yang	3	(12)
The Cell	4	(1)
The CNN Array	5	(2)
More About Templates	7	(2)
Multilayer CNNs	9	(1)
The CNN as an Analog Processor	10	(1)
Some Stability Results	11	(4)
Main Generalizations	15	(5)
Nonlinear CNNs and Delay CNNs	15	(2)
Nonuniform Processor CNNs and Multiple Neighborhood Size CNNs	17	(1)
Discrete-Time CNNs	17	(2)
The CNN Universal Machine	19	(1)
A Formal Definition	20	(3)
The Cells and Their Coupling	20	(2)
Boundary Conditions	22	(1)
Summary	23	(2)
Some Applications of CNNs	25	(18)
CNN-Based Image Pre-processing for the Automatic Classification of Fruits	25	(3)
The Pre-filtering	26	(2)
Processing of NMR Spectra	28	(7)
Two-Dimensional NMR Spectra	29	(1)
Processing of NMR Spectra with CNNs	30	(2)
Description of the Dual Algorithm	32	(3)
Air Quality Modeling	35	(5)
Models	35	(1)
CNNs for Air Quality Modeling	36	(3)
Examples	39	(1)
Conclusions	40	(3)
The CNN as a Generator of Nonlinear Dynamics	43	(36)
The State Controlled CNN Model	44	(3)
Discrete Components Realization of SC-CNN Cells	45	(2)
Chua, Oscillator Dynamics Generated by the SC-CNN	47	(4)
Main Result	47	(2)
Experimental Results	49	(2)
Chaotic Dynamics of a Colpitts Oscillator	51	(4)
Hysteresis Hyperchaotic Oscillator	55	(3)
n-Double Scroll Attractors	58	(8)
A New Realization of the n-Double Scroll Family	58	(7)
n-Double Scrolls in SC-CNNs	65	(1)
Nonlinear Dynamics Potpourri	66	(9)
A Non-autonomous Second Order Chaotic Circuit	66	(2)
A Circuit with a Nonlinear Reactive Element	68	(2)
Canards and Chaos	70	(2)
Multimode Chaos in Coupled Oscillators	72	(2)
Coupled Circuits	74	(1)
General Case and Conclusions	75	(4)
Theoretical Implications	77	(1)
Practical Implications	77	(2)
Synchronization	79	(26)
Background	79	(2)
Pecora--Carroll Approach	80	(1)
Inverse System Approach	81	(1)
Experimental Signal Transmission Using Synchronized SC-CNN	81	(12)
Circuit Description	82	(1)
Synchronization: Results of Experiment and Simulation	83	(3)
Non-ideal Channel Effects	86	(1)
Effects of Additive Noise and Disturbances on the Channel	87	(6)
Chaotic System Identification	93	(8)
Description of the Algorithm	93	(2)
Identification of the Chua Oscillator	95	(1)
Examples	96	(5)
Summary and Conclusions	101	(4)
Spatio-temporal Phenomena	105	(28)
Analysis of the Cell	105	(7)
Fixed Points	107	(2)
Limit Cycle and Bifurcations	109	(1)
Slow--Fast Dynamics	110	(2)
Some Simulation Results	112	(1)
The Two-Layer CNN	112	(3)
Traveling Wavefronts	115	(5)
Autowaves	116	(2)
Labyrinths	118	(2)
Pattern Formation	120	(7)
Condition for the Existence of Turing Patterns in Arrays of Coupled Circuits	121	(1)
Turing Patterns in the Two-Layer CNN	122	(2)
Simulation Results	124	(3)
Sensitivity to Parametric Uncertainties and Noise	127	(5)
Spiral Wave: Parametric Uncertainty	127	(2)
Spiral Waves: Presence of Noise in the Initial Conditions	129	(1)
Patterns: Parametric Uncertainties	130	(2)
Summary and Conclusions	132	(1)
Experimental CNN Setup and Applications to Motion Control	133	(34)
The Experimental Setup	134	(8)
Realization of the Cell for Autowave Generation	135	(1)
Realization of the Cell for Pattern formation	136	(2)
Realization of the Laplacian Couplings and Boundary Conditions	138	(1)
Realization of the Main Board	139	(1)
Autowave Experiments	140	(2)
Pattern Formation and Propagation	142	(7)
CNNs for Generating and Controlling Artificial Locomotion	149	(11)
Links to Biological Locomotion	149	(3)
WORMBOT: A Ring-Worm-like Walking Robot	152	(2)
REXABOT: An Hexapode Reaction-Diffusion Walking Robot	154	(5)
READIBELT: Reaction Diffusion Conveyor Belt Autowave Driven	159	(1)
Conclusion	160	(7)
Part II. Implementation and Design
A Four Quadrant S2I Switched-Current Multiplier	167	(22)
Detailed Analysis of the S2I Memory Cell	168	(5)
The Multiplier Architecture	173	(4)
Analysis and Design of the S2I Multiplier	177	(5)
Circuit Analysis of the Multiplier	177	(3)
Circuit Design	180	(2)
Experimental Performance Evaluation	182	(4)
Summary	186	(3)
A One-Dimensional Discrete-Time CNN Chip for Audio Signal Processing	189	(16)
System Architecture	189	(1)
The Tapped Delay Line	190	(2)
CNN Cells	192	(5)
Multiplier and Ancillary Circuitry	193	(4)
Cell Behavior and Hardware Multiplexing	197	(2)
Results and Example	199	(4)
Summary	203	(2)
A. Mathematical Background	205	(20)
Topology	205	(1)
Operations and Functions	206	(1)
Matrices	207	(1)
Dimension	207	(1)
Dynamical Systems: Basic Definitions	208	(1)
Steady-State Behavior	209	(3)
Classification of Asymptotic Behavior	210	(2)
Stability	212	(8)
Stability of equilibrium points	212	(5)
Stability of Limit Cycles	217	(2)
Lyapunov Exponents	219	(1)
Topological Equivalence and Conjugacy, Structural Stability and Bifurcations	220	(1)
Silnikov Method	221	(1)
Particular Results for Two-Dimensional Flows	222	(3)
B Library of Templates	225	(34)
References	259	(12)
Index	271