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.

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.

scholarly journals Dynamic Analysis of Nonlinear Impulsive Neutral Nonautonomous Differential Equations with Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jinxian Li
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Exponential Stability ◽  
Dynamic Analysis ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Lyapunov Functionals ◽  
Nonautonomous Differential Equations ◽  
Inequality Technique

A class of neural networks described by nonlinear impulsive neutral nonautonomous differential equations with delays is considered. By means of Lyapunov functionals and differential inequality technique, criteria on global exponential stability of this model are derived. Many adjustable parameters are introduced in criteria to provide flexibility for the design and analysis of the system. The results of this paper are new and they supplement previously known results. An example is given to illustrate the 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 Exponential Stability for Discrete-Time Stochastic BAM Neural Networks with Discrete and Distributed Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Analysis Problem ◽  
The Stability

This paper deals with the stability analysis problem for a class of discrete-time stochastic BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and employing M-matrix theory, we find some sufficient conditions ensuring the global exponential stability of the equilibrium point for stochastic BAM neural networks with time-varying delays. The conditions obtained here are expressed in terms of LMIs whose feasibility can be easily checked by MATLAB LMI Control toolbox. A numerical example is presented to show the effectiveness of the derived LMI-based stability conditions.

scholarly journals Existence and Global Exponential Stability of Periodic Solutions for General Neural Networks with Time-Varying Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Xinsong Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Time Varying ◽  
Inequality Techniques ◽  
Coincidence Degree Theorem

By using the coincidence degree theorem and differential inequality techniques, sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general neural networks with time-varying (including bounded and unbounded) delays. Some known results are improved and some new results are obtained. An example is employed to illustrate our feasible 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 Stability of linear neutral delay-differential systems

1988 ◽  
Vol 38 (3) ◽  
pp. 339-344 ◽  
Author(s):  
Li-Ming Li
Keyword(s):  
Differential Inequality ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

Sufficient conditions are obtained for the stability of linear neutral delay-differential systems by using a delay-differential inequality.

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.

PERIODIC SOLUTIONS FOR A CLASS OF FUZZY BAM NEURAL NETWORKS WITH DISTRIBUTED DELAYS AND VARIABLE COEFFICIENTS

2010 ◽  
Vol 20 (05) ◽  
pp. 1551-1565 ◽  
Author(s):  
YONGKUN LI ◽  
LI YANG ◽  
WANQIN WU
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Distributed Delays ◽  
Bam Neural Networks ◽  
Fuzzy Bam Neural Networks

In this paper, we consider a class of fuzzy BAM neural networks with distributed delays and variable coefficients. By using Brouwer fixed point theorem and differential inequality, we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for a class of fuzzy BAM neural networks with distributed delays and variable coefficients. In addition, we also present an illustrative example to show the effectiveness of obtained results.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

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