Existence and global exponential stability of almost periodic solution for CNNs with variable coefficients and delays

2008 ◽  
Vol 28 (1-2) ◽  
pp. 461-472 ◽  
Author(s):  
Lijuan Zhang ◽  
Bao Shi
Keyword(s):  
Periodic Solution ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Variable Coefficients ◽  
Almost Periodic Solution ◽  
Almost Periodic

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 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.

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