Global Exponential Synchronization of Complex-Valued Neural Networks with Time Delays via Matrix Measure Method

2018 ◽  
Vol 49 (1) ◽  
pp. 187-201 ◽  
Author(s):  
Dong Xie ◽  
Yueping Jiang ◽  
Minghua Han
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Exponential Synchronization ◽  
Matrix Measure ◽  
Global Exponential Synchronization ◽  
Complex Valued

scholarly journals Exponential Synchronization in Inertial Neural Networks with Time Delays

Electronics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 356 ◽  
Author(s):  
Liang Ke ◽  
Wanli Li
Keyword(s):  
Differential Equation ◽  
Neural Networks ◽  
Lyapunov Functional ◽  
Time Delays ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Inertial Neural Networks ◽  
Response Systems ◽  
Global Exponential Synchronization

In this paper, exponential synchronization for inertial neural networks with time delays is investigated. First, by introducing a directive Lyapunov functional, a sufficient condition is derived to ascertain the global exponential synchronization of the drive and response systems based on feedback control. Second, by introducing a variable substitution, the second-order differential equation is transformed into a first-order differential equation. As such, a new Lyapunov functional is constructed to formulate a novel global exponential synchronization for the systems under study. The two obtained sufficient conditions complement each other and are suitable to be applied in different cases. Finally, two numerical examples are given to illustrated the effectiveness of the proposed theoretical results.

Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 693-704 ◽  
Author(s):  
Kaifang Fei ◽  
Minghui Jiang ◽  
Meng Yan ◽  
Weizhen Liu
Keyword(s):  
Neural Networks ◽  
State Feedback ◽  
Exponential Synchronization ◽  
Matrix Measure ◽  
Analysis Techniques ◽  
Discontinuous Activations ◽  
Inclusion Theory ◽  
Generalized Halanay Inequality ◽  
New Criteria ◽  
Theoretical Results

AbstractIn this paper, the matters of dissipativity and synchronization for non-autonomous Hopfield neural networks with discontinuous activations are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. The global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, the global exponential synchronization of the addressed network drive system and the response system is realized by utilizing inequality and some analysis techniques and designing the discontinuous state feedback controller. Finally, several numerical examples are given to verify the validity of the theoretical results.

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