scholarly journals $$(\mu ,\nu )-$$Pseudo Almost Automorphic Solutions of Neutral Type Clifford-Valued High-Order Hopfield Neural Networks with D Operator

2021 ◽  
Author(s):  
Chaouki Aouiti ◽  
Farah Dridi ◽  
Qing Hui ◽  
Emmanuel Moulay
Keyword(s):  
Neural Networks ◽  
Neutral Type ◽  
High Order ◽  
Hopfield Neural Networks ◽  
D Operator ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic

scholarly journals Existence and Global Exponential Stability of Almost Automorphic Solution for Clifford-Valued High-Order Hopfield Neural Networks with Leakage Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Bing Li ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Direct Method ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Leakage Delays ◽  
Almost Automorphic

In this paper, we study the existence and global exponential stability of almost automorphic solutions for Clifford-valued high-order Hopfield neural networks by direct method. That is to say, we do not decompose the systems under consideration into real-valued systems, but we directly study Clifford-valued systems. Our methods and results are new. Finally, an example is given to illustrate our main results.

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.

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