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Cellular Neural Networks: Chaos, Complexity and VLSI Processing

Overview

The book is about new applications of cellular neural networks (CNNs), new theoretical results and implementation issues. This topic involves several scientific disciplines including circuit theory, microelectronics, dynamic systems theory and applied mathematics, information processing, biology, neurophysiology, and robotics, to cite but a few. Significant attention is paid to small-size CNNs for generating chaotic dynamics and also to their application in the area of nonlinear circuit synchronization and secure...

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Paperback (Softcover reprint of the original 1st ed. 1999)
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Overview

The book is about new applications of cellular neural networks (CNNs), new theoretical results and implementation issues. This topic involves several scientific disciplines including circuit theory, microelectronics, dynamic systems theory and applied mathematics, information processing, biology, neurophysiology, and robotics, to cite but a few. Significant attention is paid to small-size CNNs for generating chaotic dynamics and also to their application in the area of nonlinear circuit synchronization and secure communication. Complex spatio-temporal phenomena in simple CNN models are investigated. A CMOS discrete-time switched-current implementation of a CNN is presented in detail. The reader will find thorough discussion on the subject, ranging from the highest-level aspects treated in a rigorous and analytic way, to the technological challenges and the circuit design aspects.

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Editorial Reviews

From the Publisher

From the reviews:

"The book is divided into eight chapters and each of them guides us through one area where the CNNs can be used … . I recommend the publication to everybody, who is interested in the CNN and its application and implementation, but also to those who face some of the technologies described there, such as nonlinear dynamics, synchronization, signal processing or motion control, because the CNN can show a quite novel and beneficial point of view." (Václav Dekanovský, Neural Network World, Vol. 15 (5), 2005)

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Product Details

  • ISBN-13: 9783642642326
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 7/31/2012
  • Series: Springer Series in Advanced Microelectronics , #1
  • Edition description: Softcover reprint of the original 1st ed. 1999
  • Edition number: 1
  • Pages: 273
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.61 (d)

Table of Contents

I. Circuit Theory and Applications of CNNs.- 1. CNN Basics.- 1.1 The CNN of Chua and Yang.- 1.1.1 The Cell.- 1.1.2 The CNN Array.- 1.1.3 More About Templates.- 1.1.4 Multilayer CNNs.- 1.1.5 The CNN as an Analog Processor.- 1.1.6 Some Stability Results.- 1.2 Main Generalizations.- 1.2.1 Nonlinear CNNs and Delay CNNs.- 1.2.2 Nonuniform Processor CNNs and Multiple Neighborhood Size CNNs.- 1.2.3 Discrete-Time CNNs.- 1.2.4 The CNN Universal Machine.- 1.3 A Formal Definition.- 1.3.1 The Cells and Their Coupling.- 1.3.2 Boundary Conditions.- 1.4 Summary.- 2. Some Applications of CNNs.- 2.1 CNN-Based Image Pre-processing for the Automatic Classification of Fruits.- 2.1.1 The Pre-filtering.- 2.2 Processing of NMR Spectra.- 2.2.1 Two-Dimensional NMR Spectra.- 2.2.2 Processing of NMR Spectra with CNNs.- 2.2.3 Description of the Dual Algorithm.- 2.3 Air Quality Modeling.- 2.3.1 Models.- 2.3.2 CNNs for Air Quality Modeling.- 2.3.3 Examples.- 2.4 Conclusions.- 3. The CNN as a Generator of Nonlinear Dynamics.- 3.1 The State Controlled CNN Model.- 3.1.1 Discrete Components Realization of SC-CNN Cells.- 3.2 Chua Oscillator Dynamics Generated by the SC-CNN.- 3.2.1 Main Result.- 3.2.2 Experimental Results.- 3.3 Chaotic Dynamics of a Colpitts Oscillator.- 3.4 Hysteresis Hyperchaotic Oscillator.- 3.5 n-Double Scroll Attractors.- 3.5.1 A New Realization of the n-Double Scroll Family.- 3.5.2 n-Double Scrolls in SC-CNNs.- 3.6 Nonlinear Dynamics Potpourri.- 3.6.1 A Non-autonomous Second Order Chaotic Circuit.- 3.6.2 A Circuit with a Nonlinear Reactive Element.- 3.6.3 Canards and Chaos.- 3.6.4 Multimode Chaos in Coupled Oscillators.- 3.6.5 Coupled Circuits.- 3.7 General Case and Conclusions.- 3.7.1 Theoretical Implications.- 3.7.2 Practical Implications.- 4. Synchronization.- 4.1 Background.- 4.1.1 Pecora-Carroll Approach.- 4.1.2 Inverse System Approach.- 4.2 Experimental Signal Transmission Using Synchronized SC-CNN.- 4.2.1 Circuit Description.- 4.2.2 Synchronization: Results of Experiment and Simulation.- 4.2.3 Non-ideal Channel Effects.- 4.2.4 Effects of Additive Noise and Disturbances on the Channel.- 4.3 Chaotic System Identification.- 4.3.1 Description of the Algorithm.- 4.3.2 Identification of the Chua Oscillator.- 4.3.3 Examples.- 4.4 Summary and Conclusions.- 5. Spatio-temporal Phenomena.- 5.1 Analysis of the Cell.- 5.1.1 Fixed Points.- 5.1.2 Limit Cycle and Bifurcations.- 5.1.3 Slow-Fast Dynamics.- 5.1.4 Some Simulation Results.- 5.2 The Two-Layer CNN.- 5.3 Traveling Wavefronts.- 5.3.1 Autowaves.- 5.3.2 Labyrinths.- 5.4 Pattern Formation.- 5.4.1 Condition for the Existence of Turing Patterns in Arrays of Coupled Circuits.- 5.4.2 Turing Patterns in the Two-Layer CNN.- 5.4.3 Simulation Results.- 5.5 Sensitivity to Parametric Uncertainties and Noise.- 5.5.1 Spiral Wave: Parametric Uncertainty.- 5.5.2 Spiral Waves: Presence of Noise in the Initial Conditions.- 5.5.3 Patterns: Parametric Uncertainties.- 5.6 Summary and Conclusions.- 6. Experimental CNN Setup and Applications to Motion Control.- 6.1 The Experimental Setup.- 6.1.1 Realization of the Cell for Autowave Generation.- 6.1.2 Realization of the Cell for Pattern formation.- 6.1.3 Realization of the Laplacian Couplings and Boundary Conditions.- 6.1.4 Realization of the Main Board.- 6.1.5 Autowave Experiments.- 6.2 Pattern Formation and Propagation.- 6.3 CNNs for Generating and Controlling Artificial Locomotion.- 6.3.1 Links to Biological Locomotion.- 6.3.2 WORMBOT: A Ring-Worm-like Walking Robot.- 6.3.3 REXABOT: An Hexapode Reaction-Diffusion Walking Robot.- 6.3.4 READIBELT: Reaction Diffusion Conveyor Belt Autowave Driven.- 6.4 Conclusion.- II. Implementation and Design.- 7. A Four Quadrant S2I Switched-Current Multiplier.- 7.1 Detailed Analysis of the S2I Memory Cell.- 7.2 The Multiplier Architecture.- 7.3 Analysis and Design of the S2I Multiplier.- 7.3.1 Circuit Analysis of the Multiplier.- 7.3.2 Circuit Design.- 7.4 Experimental Performance Evaluation.- 7.5 Summary.- 8. A One-Dimensional Discrete-Time CNN Chip for Audio Signal Processing.- 8.1 System Architecture.- 8.2 The Tapped Delay Line.- 8.3 CNN Cells.- 8.3.1 Multiplier and Ancillary Circuitry.- 8.4 Cell Behavior and Hardware Multiplexing.- 8.5 Results and Example.- 8.6 Summary.- A. Mathematical Background.- A.1 Topology.- A.2 Operations and Functions.- A.3 Matrices.- A.4 Dimension.- A.5 Dynamical Systems: Basic Definitions.- A.6 Steady-State Behavior.- A.6.1 Classification of Asymptotic Behavior.- A.7 Stability.- A.7.1 Stability of equilibrium points.- A.7.2 Stability of Limit Cycles.- A.7.3 Lyapunov Exponents.- A.8 Topological Equivalence and Conjugacy, Structural Stability and Bifurcations.- A.9 Silnikov Method.- A.10 Particular Results for Two-Dimensional Flows.- B. Library of Templates.- References.

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