About the Authors xi
Preface xiii
Acknowledgments xvii
1 Synchronization for Complex Networks with Multiple Weights Under Recoverable Attacks 1
1.1 Introduction 1
1.2 Preliminaries 2
1.2.1 Notations 2
1.2.2 Lemmas 3
1.2.3 Network Models 3
1.3 Synchronization of CNMSCs Under Recoverable Attacks 6
1.3.1 Synchronization of CNMSCs with Directed Topology 6
1.3.2 Synchronization of CNMSCs with Undirected Topology 11
1.4 Synchronization of CNMDSCs Under Recoverable Attacks 12
1.4.1 Synchronization of CNMDSCs with Directed Topology 12
1.4.2 Synchronization of CNMDSCs with Undirected Topology 16
1.5 Numerical Examples 18
1.6 Conclusion 23
References 24
2 Passivity and Synchronization for Coupled Neural Networks with Multiweights Under PD and PI Control 29
2.1 Introduction 29
2.2 Preliminaries 31
2.2.1 Notations 31
2.2.2 Definitions 31
2.2.3 Lemma 32
2.2.4 CNNMWs 32
2.3 PD Control for Passivity and Synchronization of the CNNMWs 34
2.3.1 PD Control for Passivity of the CNNMWs 35
2.3.2 PD Control for Synchronization of the CNNMWs 38
2.4 PI Control for Passivity and Synchronization of the CNNMWs 39
2.4.1 PI Control for Passivity of the CNNMWs 40
2.4.2 PI Control for Synchronization of the CNNMWs 44
2.5 Numerical Examples 45
2.6 Conclusion 52
References 52
3 Output Synchronization for Complex Networks with Multiple Output or Output Derivative Couplings 57
3.1 Introduction 57
3.2 Output Synchronization of CDNs with Multiple Output Couplings 59
3.2.1 Network Model 59
3.2.2 Output Synchronization Analysis 61
3.2.3 Adaptive Output Synchronization 64
3.3 Output Synchronization of CDNs with Multiple Output Derivative Couplings 68
3.3.1 Network Model 68
3.3.2 Output Synchronization Analysis 68
3.3.3 Adaptive Output Synchronization 71
3.4 Numerical Examples 74
3.5 Conclusion 77
References 78
4 PD Control for Finite-Time Passivity and Synchronization of Multiweighted Complex Networks 83
4.1 Introduction 83
4.2 Preliminaries 85
4.2.1 Notations 85
4.2.2 Graph Theory 85
4.2.3 Definitions 86
4.2.4 Lemmas 86
4.2.5 MWCDNs 87
4.3 PD Control for the FTP and FTS of the CDNMSCs 88
4.3.1 FTP of the CDNMSCs 90
4.3.2 FTS of the CDNMSCs 93
4.4 PD Control for the FTP and FTS of the CDNMDCs 95
4.4.1 FTP of the CDNMDCs 96
4.4.2 FTS of the CDNMDCs 98
4.5 Numerical Examples 99
4.6 Conclusion 105
References 106
5 Finite-Time Synchronization and H ∞ Synchronization for Coupled Neural Networks with Multistate or Multiderivative Couplings 111
5.1 Introduction 111
5.2 Preliminaries 113
5.2.1 Notations 113
5.2.2 Lemmas 113
5.3 FTS and Finite-Time H ∞ Synchronization for CNNs with Multistate Couplings 114
5.3.1 FTS of CNNs with Multistate Couplings 114
5.3.2 Finite-Time H ∞ Synchronization of CNNs with Multistate Couplings and External Disturbance 118
5.4 FTS and Finite-Time H ∞ Synchronization for CNNs with Multiderivative Couplings 121
5.4.1 FTS of CNNs with Multiderivative Couplings 121
5.4.2 Finite-Time H ∞ Synchronization of CNNs with Multiderivative Couplings and External Disturbance 124
5.5 Numerical Examples 126
5.6 Conclusion 133
References 133
6 Finite-Time Synchronization and H ∞ Synchronization of Multiweighted Complex Networks with Adaptive State Couplings 137
6.1 Introduction 137
6.2 Preliminaries 139
6.2.1 Notations 139
6.2.2 Lemmas 139
6.2.3 Assumption 140
6.3 Finite-Time Synchronization and H ∞ Synchronization of Multiweighted Complex Dynamical Networks with Adaptive State Couplings 140
6.3.1 Finite-Time Synchronization 140
6.3.2 Finite-Time H ∞ Synchronization 145
6.4 Finite-Time Synchronization and H ∞ Synchronization of Multiweighted Complex Dynamical Networks with Coupling Delays and Adaptive State Couplings 148
6.4.1 Finite-Time Synchronization 148
6.4.2 Finite-Time H ∞ Synchronization 153
6.5 Numerical Examples 157
6.6 Conclusion 163
References 163
7 Finite-Time Output Synchronization and H ∞ Output Synchronization of Coupled Neural Networks with Multiple Output Couplings 169
7.1 Introduction 169
7.2 Preliminaries 171
7.2.1 Notations 171
7.2.2 Lemmas 171
7.3 Finite-Time Output Synchronization of CNNMOC 172
7.3.1 Fixed Coupling Weights 172
7.3.2 Adaptive Coupling Weights 177
7.4 Finite-Time H ∞ Output Synchronization of CNNMOC 181
7.4.1 Fixed Coupling Weights 181
7.4.2 Adaptive Coupling Weights 185
7.5 Numerical Examples 189
7.6 Conclusion 194
References 194
8 Finite-Time Passivity and Synchronization of Coupled Reaction–Diffusion Neural Networks with Multiple Weights 199
8.1 Introduction 199
8.2 Preliminaries 201
8.2.1 Notations 201
8.2.2 Lemmas 201
8.2.3 Definitions 202
8.3 Finite-Time Passivity and Synchronization of CRDNNs with Multiple Weights 203
8.3.1 Network Model 203
8.3.2 Finite-Time Passivity 204
8.3.3 Finite-Time Synchronization 209
8.4 Finite-Time Passivity and Synchronization of CRDNNs with Multiple Coupling Delays 211
8.4.1 Network Model 211
8.4.2 Finite-Time Passivity 211
8.4.3 Finite-Time Synchronization 215
8.5 Numerical Examples 218
8.6 Conclusion 224
References 225
Index 229
