Convergence analysis of recurrent neural networks
By: Zhang Yi, K.K. Tan.
Contributors: Tan, K. K.
Series: Network theory and applications -- v. 13.
Publisher: Kluwer Academic Publishers
Published: 2004
Place of publication: Boston
Language: eng
Number of pages: 233
Subjects: Neural networks (Computer science)
Notes: Includes bibliographical references (p. 219-233).
Table of contents: title: List of Figures
pagenum: ix; title: Preface
pagenum: xi; title: Acknowledgments
pagenum: xv; label: 1
title: Introduction
pagenum: 1; label: 1
title: Introduction
pagenum: 1; label: 1.1
title: Recurrent Neural Networks
pagenum: 1; label: 1.2
title: Convergence of RNNs
pagenum: 2; label: 1.3
title: Outline of the Book
pagenum: 4; label: 2
title: Some Notations and Terminologies
pagenum: 7; label: 3
title: Energy Functions Method for Convergence Analysis
pagenum: 8; label: 3.1
title: Energy Functions
pagenum: 8; label: 3.2
title: Relationships Between Minimums of Energy Functions and Equilibria of Networks
pagenum: 11; label: 4
title: Conclusions
pagenum: 14; label: 2
title: Hopfield Recurrent Neural Networks
pagenum: 15; label: 1
title: Introduction
pagenum: 15; label: 2
title: Equilibria Analysis
pagenum: 17; label: 3
title: Complete Stability
pagenum: 20; label: 4
title: Global Convergence
pagenum: 21; label: 4.1
title: Global Asymptotic Stability
pagenum: 22; label: 4.2
title: Global Exponential Stability
pagenum: 23; label: 5
title: Local Exponential Convergence
pagenum: 27; label: 5.1
title: Example
pagenum: 29; label: 6
title: Discussions and Conclusions
pagenum: 31; label: 3
title: Cellular Neural Networks
pagenum: 33; label: 1
title: Introduction
pagenum: 33; label: 2
title: Properties of Output Function
pagenum: 34; label: 3
title: Standard CNNs
pagenum: 37; label: 3.1
title: The Standard CNN Model
pagenum: 37; label: 3.2
title: Equilibria Analysis
pagenum: 38; label: 3.3
title: Complete Stability of CNNs
pagenum: 40; label: 3.4
title: Global Exponential Stability and Convergence Rate Estimation
pagenum: 45; label: 4
title: CNNs with Constant Delays
pagenum: 50; label: 4.1
title: Model of CNNs with Constant Delays
pagenum: 51; label: 4.2
title: Conditions for GES
pagenum: 52; label: 5
title: CNNs with Infinite Delay
pagenum: 54; label: 5.1
title: Model of CNNs with Infinite Delay
pagenum: 54; label: 5.2
title: Preliminaries
pagenum: 55; label: 5.3
title: Relations Between State Stability and Output Stability
pagenum: 56; label: 5.4
title: Global Convergence Analysis
pagenum: 59; label: 5.5
title: Examples
pagenum: 65; label: 6
title: Conclusions
pagenum: 66; label: 4
title: Recurrent Neural Networks with Unsaturating Piecewise Linear Activation Functions
pagenum: 69; label: 1
title: Introduction
pagenum: 69; label: 2
title: Preliminaries
pagenum: 71; label: 3
title: Multistability Analysis
pagenum: 74; label: 3.1
title: Boundedness and Global Attractivity
pagenum: 74; label: 3.2
title: Complete Stability
pagenum: 81; label: 4
title: Simulation Examples
pagenum: 84; label: 5
title: Conclusions
pagenum: 89; label: 5
title: Lotka-Volterra Recurrent Neural Networks with Delays
pagenum: 91; label: 1
title: Introduction
pagenum: 91; label: 2
title: Multistability Analysis
pagenum: 92; label: 2.1
title: Preliminaries
pagenum: 92; label: 2.2
title: Boundedness and Global Attractivity
pagenum: 94; label: 2.3
title: Complete Convergence
pagenum: 99; label: 2.4
title: Simulations and Examples
pagenum: 103; label: 3
title: Monostability Analysis
pagenum: 104; label: 3.1
title: Preliminaries
pagenum: 104; label: 3.2
title: Positive Lower Boundedness
pagenum: 106; label: 3.3
title: Exponential Convergence
pagenum: 110; label: 3.4
title: Asymptotic Convergence
pagenum: 112; label: 3.5
title: Simulation Results
pagenum: 115; label: 4
title: Conclusions
pagenum: 117; label: 6
title: Delayed Recurrent Neural Networks with Global Lipschitz Activation Functions
pagenum: 119; label: 1
title: Introduction
pagenum: 119; label: 1.1
title: Global Lipschitz Activation Functions
pagenum: 119; label: 1.2
title: Functional Differential Equations
pagenum: 121; label: 1.3
title: Organisations
pagenum: 121; label: 2
title: RNNs with Constant Delays
pagenum: 122; label: 2.1
title: Preliminaries
pagenum: 122; label: 2.2
title: Convergence Rate Estimate
pagenum: 124; label: 2.3
title: Global Exponential Stability
pagenum: 128; label: 2.4
title: Discussions and Illustrative Examples
pagenum: 129; label: 2.5
title: Conclusions
pagenum: 130; label: 3
title: RNNs with Variable Delays
pagenum: 131; label: 3.1
title: Preliminaries
pagenum: 131; label: 3.2
title: Convergence Analysis
pagenum: 132; label: 3.3
title: Examples and Discussions
pagenum: 138; label: 3.4
title: Conclusions
pagenum: 140; label: 4
title: Special RNN Model with Delays
pagenum: 140; label: 4.1
title: Preliminaries
pagenum: 140; label: 4.2
title: Equilibrium Point and Convergence Analysis
pagenum: 142; label: 4.3
title: Examples and Discussions
pagenum: 148; label: 4.4
title: Conclusions
pagenum: 150; label: 5
title: Absolute Stability and Absolute Periodicity
pagenum: 150; label: 5.1
title: Preliminaries
pagenum: 151; label: 5.2
title: Main Results
pagenum: 154; label: 5.3
title: Simulation Study on Absolute Periodicity
pagenum: 159; label: 5.4
title: Conclusions
pagenum: 162; label: 6
title: Bidirectional Associative Memory RNNs with Delays
pagenum: 163; label: 6.1
title: Equilibrium Points and Stability Analysis
pagenum: 163; label: 6.2
title: Stable Periodic Trajectories
pagenum: 168; label: 6.3
title: Discussions and Examples
pagenum: 169; label: 7
title: Other Models of Continuous Time Recurrent Neural Networks
pagenum: 171; label: 1
title: RNNs with Variable Inputs
pagenum: 171; label: 1.1
title: Introduction
pagenum: 171; label: 1.2
title: Preliminaries
pagenum: 173; label: 1.3
title: Convergence Analysis
pagenum: 174; label: 1.4
title: Examples
pagenum: 181; label: 2
title: RNN Model for Extracting Eigenvectors
pagenum: 183; label: 2.1
title: Introduction
pagenum: 183; label: 2.2
title: Equilibrium Points Analysis
pagenum: 184; label: 2.3
title: Representation of Solutions
pagenum: 185; label: 2.4
title: Convergence Analysis
pagenum: 187; label: 2.5
title: Examples and Simulation Results
pagenum: 190; label: 8
title: Discrete Recurrent Neural Networks
pagenum: 195; label: 1
title: Introduction
pagenum: 195; label: 2
title: Discrete RNNs with Unsaturating Piecewise Linear Activation Functions
pagenum: 196; label: 2.1
title: Preliminaries
pagenum: 197; label: 2.2
title: Boundedness and Global Attractivity
pagenum: 199; label: 2.3
title: Complete Convergence
pagenum: 201; label: 2.4
title: Simulation Examples
pagenum: 205; label: 3
title: Discrete RNN Model for Winner Take All Problem
pagenum: 208; label: 3.1
title: Neural Network Model
pagenum: 209; label: 3.2
title: Dynamic Properties
pagenum: 210; label: 3.3
title: Network Response Time
pagenum: 214; label: 3.4
title: Simulations
pagenum: 215