scholarly journals Global Exponential Stability of Antiperiodic Solution for Impulsive High-Order Hopfield Neural Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wei Chen ◽  
Shuhua Gong
Keyword(s):  
Neural Networks ◽  
Theoretical Result ◽  
Exponential Stability ◽  
Numerical Simulations ◽  
Global Exponential Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Distributed Delays ◽  
Leakage Delays

This paper is concerned with antiperiodic solutions for impulsive high-order Hopfield neural networks with leakage delays and continuously distributed delays. By employing a novel proof, some sufficient criteria are established to ensure the existence and global exponential stability of the antiperiodic solution, which are new and complement of previously known results. Moreover, an example and numerical simulations are given to support the theoretical result.

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.

scholarly journals Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays

2021 ◽  
Vol 7 (3) ◽  
pp. 3653-3679
Author(s):  
Nina Huo ◽  
◽  
Bing Li ◽  
Yongkun Li ◽  
◽  
...  
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Banach Fixed Point Theorem ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic

<abstract><p>In this paper, we consider a class of Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays whose coefficients are Clifford numbers except the time delays. Based on the Banach fixed point theorem and inequality techniques, we obtain the existence and global exponential stability of almost periodic solutions in distribution of this class of neural networks. Even if the considered neural networks degenerate into real-valued, complex-valued and quaternion-valued ones, our results are new. Finally, we use a numerical example and its computer simulation to illustrate the validity and feasibility of our theoretical results.</p></abstract>

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