《Qualitative Analysis and Control ofComplex Neural Networks with Delays》以復雜神經(jīng)網(wǎng)絡定性穩(wěn)定性研究為核心，并結(jié)合定量研究深入展開，形成容納復雜網(wǎng)絡和多智能體系統(tǒng)的動態(tài)特性的研究脈絡。《Qualitative Analysis and Control ofComplex Neural Networks with Delays》的特點是在動力系統(tǒng)和穩(wěn)定性之間的關系上進行了詳盡的闡述，傳統(tǒng)的動力神經(jīng)網(wǎng)絡和當下的復雜神經(jīng)網(wǎng)絡及多智能體之間的關系進行闡述，揭示了大規(guī)模系統(tǒng)之間的演化關系。同時，針對單穩(wěn)定性、多穩(wěn)定性、周期解和不變集等動態(tài)特性進行相互關系研究，并將所得到的結(jié)果用到動力系統(tǒng)的同步性和一致性方面。結(jié)合動力系統(tǒng)的這些特點，將神經(jīng)網(wǎng)絡的動態(tài)特性應用到聯(lián)想記憶、模式識別、在線計算及進化學習等方面具體的應用方面，實現(xiàn)神經(jīng)網(wǎng)絡理論和實際問題的零距離結(jié)合
作者簡介
暫缺《Qualitative Analysis and Control of Complex Neu》作者簡介
圖書目錄
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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