Existence and global exponential stability of almost periodic solution for quaternion‐valued high‐order Hopfield neural networks with delays via a direct method

2020 ◽  
Vol 43 (10) ◽  
pp. 6165-6180 ◽  
Author(s):  
Yongkun Li ◽  
Jianglian Xiang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Direct Method ◽  
Almost Periodic Solution ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Almost Periodic ◽  
A Direct Method

scholarly journals Almost Periodic Solution for Memristive Neural Networks with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Huaiqin Wu ◽  
Luying Zhang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Almost Periodic Solution ◽  
Time Varying ◽  
Almost Periodic ◽  
Memristive Neural Networks ◽  
The Stability ◽  
Stability Issues

This paper is concerned with the dynamical stability analysis for almost periodic solution of memristive neural networks with time-varying delays. Under the framework of Filippov solutions, by applying the inequality analysis techniques, the existence and asymptotically almost periodic behavior of solutions are discussed. Based on the differential inclusions theory and Lyapunov functional approach, the stability issues of almost periodic solution are investigated, and a sufficient condition for the existence, uniqueness, and global exponential stability of the almost periodic solution is established. Moreover, as a special case, the condition which ensures the global exponential stability of a unique periodic solution is also presented for the considered memristive neural networks. Two examples are given to illustrate the validity of the theoretical results.

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 of Almost Periodic Solution for Neutral-Type Cohen-Grossberg Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Lijun Xu ◽  
Qi Jiang ◽  
Guodong Gu
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Neutral Type ◽  
Impulsive Differential Equations ◽  
Cellular Neural Networks ◽  
Almost Periodic Solution ◽  
Distributed Delays ◽  
Almost Periodic

A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the 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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