1 Introduction to Neural Networks
1.1 Natural and Artificial Neural Networks
1.2 Models of Computation
1.3 Networks of Neurons
1.4 Associative Memory Networks
1.5 Hopfield Neural Networks
1.6 Cohen-Grossberg Neural Networks
1.7 Property of Neural Network
1.8 Information Processing Capacity of Dynamical Systems
1.9 Stability of Dynamical Neural Networks
1.10 Delay Effects on Dynamical Neural Networks
1.11 Features of LMI-Based Stability Results
1.12 Summary
References
2 Preliminaries on Dynamical Systems and Stability Theory
2.1 Overview of Dynamical Systems
2.2 Definition of Dynamical System and Its Qualitative Analysis
2.3 Lyapunov Stability of Dynamical Systems
2.4 Stability Theory
2.5 Applications of Dynamical Systems Theory
2.6 Notations and Discussions on Some Stability Problems
2.6.1 Notations and Preliminaries
2.6.2 Discussions on Some Stability Definitions
2.7 Summary
References
3 Survey of Dynamics of Cohen-Grossberg-Type RNNs
3.1 Introduction
3.2 Main Research Directions of Stability of RNNs
3.2.1 Development of Neuronal Activation Functions
3.2.2 Evolution of Uncertainties in Interconnection Matrix
3.2.3 Evolution of Time Delays
3.2.4 Relations Between Equilibrium and Activation Functions
3.2.5 Different Construction Methods of Lyapunov Functions
3.2.6 Expression Forms of Stability Criteria
3.2.7 Domain of Attraction
3.2.8 Different Kinds of Neural Network Models
3.3 Stability Analysis for Cohen-Grossberg-Type RNNs
3.3.1 Stability on Hopfield-Type RNNs
3.3.2 Stability on Cohen-Grossberg-Type RNNs
3.3.3 The Case with Nonnegative Equilibria
3.3.4 Stability via M-Matrix or Algebraic Inequality Methods
3.3.5 Stability via Matrix Inequalities or Mixed Methods
3.3.6 Topics on Robust Stability of RNNs
3.3.7 Other Topics on Stability Results of RNNs
3.3.8 Qualitative Evaluation on the Stability Results of RNNs
3.4 Necessary and Sufficient Conditions for RNNs
3.5 Summary
References
4 Delay-Partitioning-Method Based Stability Results for RNNs
4.1 Introduction
4.2 Problem Formulation
4.3 GAS Criteria with Single Weighting-Delay
4.3.1 Weighting-Delay-Independent Stability Criterion
4.3.2 Weighting-Delay-Dependent Stability Criterion
4.4 GAS Criteria with Multiple Weighting-Delays
4.5 Implementation of Optimal Weighting-Delay Parameters
4.5.1 The Single Weighting-Delay Case
4.5.2 The Multiple Weighting-Delays Case
4.6 Illustrative Examples
4.7 Summary
References
5 Stability Criteria for RNNs Based on Secondary Delay Partitioning
5.1 Introduction
5.2 Problem Formulation and Preliminaries
5.3 Global Asymptotical Stability Result
5.4 Illustrative Example
5.5 Summary
References
6 LMI-Based Stability Criteria for Static Neural Networks
6.1 Introduction
6.2 Problem Formulation
6.3 Main Results
6.4 Illustrative Example
6.5 Summary
References
7 Multiple Stability for Discontinuous RNNs
7.1 Introduction
7.2 Problem Formulations and Preliminaries
7.3 Main Results
7.4 Illustrative Examples
7.5 Summary
References
8 LMI-based Passivity Criteria for RNNs with Delays
8.1 Introduction
8.2 Problem Formulation
8.3 Passivity for RNNs Without Uncertainty
8.4 Passivity for RNNs with Uncertainty
8.5 Illustrative Examples
8.6 Summary
References
9 Dissipativity and Invariant Sets for Neural Networks with Delay
9.1 Delay-Dependent Dissipativity Conditions for Delayed RNNs
9.1.1 Introduction
9.1.2 Problem Formulation
9.1.3 0-dissipativity Result
9.2 Positive Invariant Sets and Attractive Sets of DNN
9.2.1 Introduction
9.2.2 Problem Formulation and Preliminaries
9.2.3 Invariant Set Results
9.3 Attracting and Invariant Sets of CGNN with Delays
9.3.1 Introduction
9.3.2 Problem Formulation and Preliminaries
9.3.3 Invariant Set Result
9.4 Summary
References
10 Synchronization Stability in Complex Neural Networks
10.1 Introduction
10.2 Problem Formulation and Preliminaries
10.3 Synchronization Results
10.4 Illustrative Example
10.5 Summary
References
11 Stabilization of Stochastic RNNs with Stochastic Delays
11.1 Introduction
11.2 Problem Formulation and Preliminaries
11.3 Stabilization Result
11.4 Illustrative Examples
11.5 Summary
References
12 Adaptive Synchronization of Complex Neural Networks
12.1 Introduction
12.2 Problem Formulation and Preliminaries
12.3 Adaptive Synchronization Scheme
12.4 Illustrative Example
12.5 Summary
References
Index
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