Dynamical Behaviors of Multiweighted Complex Network Systems

Jin-Liang Wang, PhD, is a Professor with the School of Computer Science and Technology, Tiangong University, Tianjin, China. Shun-Yan Ren, PhD, is a Postdoctoral Research Fellow with the School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, China. Huai-Ning Wu, PhD, is a Professor with Beihang University and a Distinguished Professor of Yangtze River Scholar with the Ministry of Education of China. Tingwen Huang, PhD, is a Professor at Texas A&M University at Qatar.

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 17

1.6 Conclusion 23

References 23

2 Passivity and synchronization for coupled neural networks with multiweights under PD and PI control 27

2.1 Introduction 27

2.2 Preliminaries 29

2.2.1 Notations 29

2.2.2 Definitions 29

2.2.3 Lemma 30

2.2.4 CNNMWs 30

2.3 PD control for passivity and synchronization of the CNNMWs 32

2.3.1 PD control for passivity of the CNNMWs 33

2.3.2 PD control for synchronization of the CNNMWs 36

2.4 PI control for passivity and synchronization of the CNNMWs 37

2.4.1 PI control for passivity of the CNNMWs 38

2.4.2 PI control for synchronization of the CNNMWs 42

2.5 Numerical examples 43

2.6 Conclusion 50

References 50

3 Output synchronization for complex networks with multiple output or output derivative couplings 55

3.1 Introduction 55

3.2 Output synchronization of CDNs with multiple output couplings 57

3.2.1 Network model 57

3.2.2 Output synchronization analysis 58

3.2.3 Adaptive output synchronization 62

3.3 Output synchronization of CDNs with multiple output derivative couplings 66

3.3.1 Network model 66

3.3.2 Output synchronization analysis 66

3.3.3 Adaptive output synchronization 69

3.4 Numerical examples 72

3.5 Conclusion 76

References 76

4 PD control for finite-time passivity and synchronization of multiweighted complex networks 81

4.1 Introduction 81

4.2 Preliminaries 83

4.2.1 Notations 83

4.2.2 Graph theory 83

4.2.3 Definitions 84

4.2.4 Lemmas 84

4.2.5 MWCDNs 85

4.3 PD control for the FTP and FTS of the CDNMSCs 86

4.3.1 FTP of the CDNMSCs 87

4.3.2 FTS of the CDNMSCs 91

4.4 PD control for the FTP and FTS of the CDNMDCs 92

4.4.1 FTP of the CDNMDCs 93

4.4.2 FTS of the CDNMDCs 96

4.5 Numerical examples 97

4.6 Conclusion 103

References 103

5 Finite-time synchronization and H synchronization for coupled neural networks with multistate or

multiderivative couplings 107

5.1 Introduction 107

5.2 Preliminaries 109

5.2.1 Notations 109

5.2.2 Lemmas 109

5.3 FTS and finite-time H synchronization for CNNs with multistate couplings 109

5.3.1 FTS of CNNs with multistate couplings 110

5.3.2 Finite-time H synchronization of CNNs with multistate couplings and external disturbance 114

5.4 FTS and finite-time H synchronization for CNNs with multiderivative couplings 116

5.4.1 FTS of CNNs with multiderivative couplings 117

5.4.2 Finite-time H synchronization of CNNs with multiderivative couplings and external disturbance 119

5.5 Numerical examples 122

5.6 Conclusion 128

References 128

6 Finite-time synchronization and H synchronization of multiweighted complex networks with adaptive state couplings 133

6.1 Introduction 133

6.2 Preliminaries 135

6.2.1 Notations 135

6.2.2 Lemmas 135

6.2.3 Assumption 136

6.3 Finite-time synchronization and H synchronization of multiweighted complex dynamical networks with adaptive state couplings 136

6.3.1 Finite-time synchronization 136

6.3.2 Finite-time H synchronization 141

6.4 Finite-time synchronization and H synchronization of multiweighted complex dynamical networks with coupling delays and adaptive state couplings 144

6.4.1 Finite-time synchronization 144

6.4.2 Finite-time H synchronization 149

6.5 Numerical examples 152

6.6 Conclusion 159

References 159

7 Finite-time output synchronization and H output synchronization of coupled neural networks with multiple output couplings 165

7.1 Introduction 165

7.2 Preliminaries 167

7.2.1 Notations 167

7.2.2 Lemmas 167

7.3 Finite-time output synchronization of CNNMOC 168

7.3.1 Fixed coupling weights 168

7.3.2 Adaptive coupling weights 173

7.4 Finite-time H output synchronization of CNNMOC 177

7.4.1 Fixed coupling weights 177

7.4.2 Adaptive coupling weights 181

7.5 Numerical examples 185

7.6 Conclusion 188

References 190

8 Finite-time passivity and synchronization of coupled reaction-diffusion neural networks with multiple weights 195 8.1 Introduction 195

8.2 Preliminaries 197

8.2.1 Notations 197

8.2.2 Lemmas 197

8.2.3 Definitions 198

8.3 Finite-time passivity and synchronization of CRDNNs with multiple weights 198

8.3.1 Network model 198

8.3.2 Finite-time passivity 199

8.3.3 Finite-time synchronization 205

8.4 Finite-time passivity and synchronization of CRDNNs with multiple coupling delays 207

8.4.1 Network model 207

8.4.2 Finite-time passivity 207

8.4.3 Finite-time synchronization 211

8.5 Numerical examples 214

8.6 Conclusion 220

References 220