Global Asymptotic Stability of Periodic Solutions for Discrete Time Delayed BAM Neural Networks by Combining Coincidence Degree Theory with LMI Method

2018 ◽  
Vol 50 (2) ◽  
pp. 1321-1340 ◽  
Author(s):  
Ling Ren ◽  
Xuejun Yi ◽  
Zhengqiu Zhang
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Discrete Time ◽  
Global Asymptotic Stability ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Bam Neural Networks

scholarly journals Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1055 ◽  
Author(s):  
Manickam Iswarya ◽  
Ramachandran Raja ◽  
Grienggrai Rajchakit ◽  
Jinde Cao ◽  
Jehad Alzabut ◽  
...  
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Bam Neural Networks ◽  
Graph Theoretic

In this work, a general class of discrete time bidirectional associative memory (BAM) neural networks (NNs) is investigated. In this model, discrete and continuously distributed time delays are taken into account. By utilizing this novel method, which incorporates the approach of Kirchhoff’s matrix tree theorem in graph theory, Continuation theorem in coincidence degree theory and Lyapunov function, we derive a few sufficient conditions to ensure the existence, uniqueness and exponential stability of the periodic solution of the considered model. At the end of this work, we give a numerical simulation that shows the effectiveness of this work.

scholarly journals Existence and stability of periodic solutions for a class of generalized nonautonomous neural networks with distributed delays

2005 ◽  
Vol 2005 (7) ◽  
pp. 997-1005
Author(s):  
Yongkun Li ◽  
Lifei Zhu ◽  
Wenxiang Liu
Keyword(s):  
Neural Networks ◽  
Global Stability ◽  
Periodic Solutions ◽  
Lyapunov Functions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Distributed Delays ◽  
Coincidence Degree Theory ◽  
Existence And Stability

By using the continuation theorem of coincidence degree theory and Lyapunov functions, we study the existence and global stability of periodic solutions for a class of generalized nonautonomous neural networks with distributed delays.

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