scholarly journals Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays

2021 ◽  
Author(s):  
Yonghui Chen ◽  
Xian Zhang ◽  
Yu Xue
Keyword(s):  
Neural Networks ◽  
High Order ◽  
Exponential Synchronization ◽  
Hopfield Neural Networks ◽  
Distributed Delays ◽  
Time Varying ◽  
Discrete Delays ◽  
Unbounded Distributed Delays ◽  
Global Exponential Synchronization

Almost automorphic synchronization of quaternion-valued high-order Hopfield neural networks with time-varying and distributed delays

2018 ◽  
Vol 36 (3) ◽  
pp. 983-1013 ◽  
Author(s):  
Yongkun Li ◽  
Huimei Wang ◽  
Xiaofang Meng
Keyword(s):  
Neural Networks ◽  
Lyapunov Functions ◽  
State Feedback ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Distributed Delays ◽  
Banach Fixed Point Theorem ◽  
Time Varying ◽  
Almost Automorphic ◽  
Quaternion Multiplication

AbstractIn this paper, we consider the problem of the almost automorphic synchronization of quaternion-valued high-order Hopfield neural networks (QVHHNNs) with time-varying and distributed delays. Firstly, to avoid the non-commutativity of quaternion multiplication, we decompose QVHHNNs into an equivalent real-valued system. Secondly, we use the Banach fixed point theorem to obtain the existence of almost automorphic solutions of QVHHNNs. Thirdly, by designing a novel state-feedback controller and constructing suitable Lyapunov functions, we obtain that the drive-response structure of QVHHNNs with almost automorphic coefficients can realize the exponential synchronization. Our results are completely new. Finally, a numerical example is given to illustrate the feasibility of our results.

scholarly journals LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yangfan Wang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Global Exponential Robust Stability

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

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