Dynamical Behaviors of Multiweighted Complex Network Systems

Highly comprehensive resource for studying neural networks, complex networks, synchronization, passivity, and associated applications

Dynamical Behaviors of Multiweighted Complex Network Systems discusses the dynamical behaviors of various multiweighted complex dynamical networks, with detailed insight on synchronization for directed and undirected complex networks (CNs) with multiple state or delayed state couplings subject to recoverable attacks, along with passivity and synchronization for coupled neural networks with multi-weights (CNNMWs) by virtue of devised proportional-integral-derivative (PID) controllers.

The book also investigates finite-time synchronization (FTS) and H-infinity synchronization for two types of coupled neural networks (CNNs) and focuses on finite-time passivity (FTP) and finite-time synchronization (FTS) for complex dynamical networks with multiple state/derivative couplings based on the proportional-derivative (PD) control method. Final chapters consider finite-time output synchronization and H-infinity output synchronization problems, and multiple weighted coupled reaction-diffusion neural networks (CRDNNs) with and without coupling delays.

Other topics covered in Dynamical Behaviors of Multiweighted Complex Network Systems include:

• Criteria of FTP for complex dynamical networks with multiple state couplings (CDNMSCs), formulated by utilizing the PD controller
• Finite-time passivity (FTP) concepts for the spatially and temporally systems with different dimensions of output and input
• FTS and finite time H-infinity synchronization problems for CDNs with multiple state/derivative couplings by utilizing state feedback control approach and selecting suitable parameter adjustment schemes
• Adaptive output synchronization and output synchronization of CDNs with multiple output or output derivative couplings, and other adaptive control schemes

Enabling readers to understand foundational concepts and grasp the latest research, Dynamical Behaviors of Multiweighted Complex Network Systems is essential for all who study neural networks, complex networks, synchronization, passivity, and their applications.

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

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.