scholarly journals Attracting and Quasi-Invariant Sets of Cohen-Grossberg Neural Networks with Time Delay in the Leakage Term under Impulsive Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Differential Inequality ◽  
Invariant Sets ◽  
Leakage Term ◽  
Impulsive Perturbations ◽  
Delay Differential ◽  
Delay Differential Inequality

A class of impulsive Cohen-Grossberg neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, the attracting and invariant sets of the networks are obtained. The results in this paper extend and improve the earlier publications. An example is presented to illustrate the effectiveness of our conclusion.

scholarly journals Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Leakage Term ◽  
Interval Neural Networks ◽  
Global Exponential Robust Stability ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

Impulsive and Diffusive Effects on Stability of BAM Neural Networks with Delays

2011 ◽  
Vol 219-220 ◽  
pp. 896-899
Author(s):  
Qing Hua Zhou ◽  
Li Wan
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Bam Neural Networks ◽  
Bidirectional Associative Memory ◽  
Diffusion Effects ◽  
Impulsive Delay ◽  
Diffusive Effects ◽  
Delay Differential ◽  
Delay Differential Inequality

Although the results on exponential stability of delayed bidirectional associative memory (BAM) neural networks with impulse or diffusion were reported by some researchers, impulsive and diffusive effects should simultaneously be taken account into consideration since diffusion and impulses are ubiquitous in both nature and manmade systems, which reflects a more realistic dynamics than the former results. By using the impulsive delay differential inequality, some new sufficient criteria on exponential stability are established. Our criteria are independent of diffusion effects and dependent on the magnitude of the delays and impulses, which shows that diffusion effects are harmless and the magnitude of the delays and impulses needs enough small in the stabilization.

scholarly journals Synchronization Analysis of a Class of Neural Networks with Multiple Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Changyou Wang ◽  
Qiang Yang ◽  
Tao Jiang ◽  
Nan Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Lyapunov Function ◽  
Differential Inequality ◽  
Time Delays ◽  
Multiple Delays ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Delay Differential ◽  
Delay Differential Inequality

In this paper, we study the synchronization of a new fractional-order neural network with multiple delays. Based on the control theory of linear systems with multiple delays, we get the controller to analyse the synchronization of the system. In addition, a suitable Lyapunov function is constructed by using the theory of delay differential inequality, and some criteria ensuring the synchronization of delay fractional neural networks with Caputo derivatives are obtained. Finally, the accuracy of the method is verified by a numerical example.

GLOBAL EXPONENTIAL STABILITY CONDITIONS FOR DELAYED PARABOLIC NEURAL NETWORKS WITH VARIABLE COEFFICIENTS

2007 ◽  
Vol 17 (12) ◽  
pp. 4409-4415
Author(s):  
XUYANG LOU ◽  
BAOTONG CUI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Lyapunov Functionals ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

In this paper, we present a class of delayed parabolic neural networks (DPNN) with variable coefficients. Some sufficient conditions for the global exponential stability of the DPNN with variable coefficients are derived by a method based on delay differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of DPNN with variable coefficients.

DELAY INDEPENDENT AND DEPENDENT STABILITY ANALYSIS FOR COHEN–GROSSBERG NEURAL NETWORKS WITH TIME-VARYING DELAYS

2009 ◽  
Vol 19 (09) ◽  
pp. 3149-3159
Author(s):  
YIGUANG LIU ◽  
ZHISHENG YOU ◽  
BINGBING LIU
Keyword(s):  
Neural Networks ◽  
Global Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Time Varying ◽  
Activation Functions ◽  
Delay Differential ◽  
Delay Dependent ◽  
Delay Differential Inequality

For Cohen–Grossberg neural networks with time-varying delays, by fixed point and contract mapping theorems, a sufficient condition ensuring the existence and uniqueness of an equilibrium is proposed. To guarantee the delay independent global stability of the equilibrium, two sufficient conditions are proposed by means of a time delay differential inequality and contradiction tricks, respectively. By virtue of a special Lyapunov functional as well as properties of M-matrices, a sufficient condition undertaking the delay dependent global stability of the equilibrium is introduced. Compared with known literatures, the presented results place slack restrictions on the activation functions, and are suitable for the networks with time-varying delays. Furthermore, most of the obtained results are independent of the amplification functions, making their applicability more far-reaching. Finally, two examples are numerically simulated to illustrate the validity as well as novelty of the criteria.

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