Global Exponential Stability of High-Order Neural Networks with Time-Varying Coefficients and Delays

2010 ◽  
Author(s):  
Jie Zhou ◽  
Huanxing Cai
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
High Order ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Varying Coefficients

scholarly journals Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality

2013 ◽  
Vol 23 (1) ◽  
pp. 201-211 ◽  
Author(s):  
Yang Liu ◽  
Rongjiang Yang ◽  
Jianquan Lu ◽  
Bo Wu ◽  
Xiushan Cai
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
High Order ◽  
Impulsive Effect ◽  
Time Varying ◽  
Stability Criteria ◽  
Globally Exponential Stability ◽  
Impulsive Differential Inequality

This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous results. Finally, two numerical examples are given to illustrate the advantages of the obtained results.

Global exponential stability of cellular neural networks with multi-proportional delays

2015 ◽  
Vol 08 (06) ◽  
pp. 1550071 ◽  
Author(s):  
Liqun Zhou ◽  
Yanyan Zhang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Varying Coefficients ◽  
Proportional Delays ◽  
Time Varying Coefficients ◽  
Delay Differential ◽  
Delay Dependent

In this paper, a class of cellular neural networks (CNNs) with multi-proportional delays is studied. The nonlinear transformation yi(t) = xi( e t) transforms a class of CNNs with multi-proportional delays into a class of CNNs with multi-constant delays and time-varying coefficients. By applying Brouwer fixed point theorem and constructing the delay differential inequality, several delay-independent and delay-dependent sufficient conditions are derived for ensuring the existence, uniqueness and global exponential stability of equilibrium of the system and the exponentially convergent rate is estimated. And several examples and their simulations are given to illustrate the effectiveness of obtained 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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