scholarly journals Global Exponential Stability of Discrete-Time Multidirectional Associative Memory Neural Network with Variable Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Min Wang ◽  
Tiejun Zhou ◽  
Xiaolan Zhang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Associative Memory ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Sufficient Condition ◽  
Variable Delays ◽  
Exponentially Stable ◽  
Inequality Technique

A discrete-time multidirectional associative memory neural networks model with varying time delays is formulated by employing the semidiscretization method. A sufficient condition for the existence of an equilibrium point is given. By calculating difference and using inequality technique, a sufficient condition for the global exponential stability of the equilibrium point is obtained. The results are helpful to design global exponentially stable multidirectional associative memory neural networks. An example is given to illustrate the effectiveness of the results.

A NOVEL GLOBAL EXPONENTIAL STABILITY RESULT FOR DISCRETE-TIME CELLULAR NEURAL NETWORKS WITH VARIABLE DELAYS

2006 ◽  
Vol 16 (06) ◽  
pp. 467-472 ◽  
Author(s):  
QIANG ZHANG ◽  
XIAOPENG WEI ◽  
JIN XU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Stability Condition ◽  
Global Exponential Stability ◽  
Stability Result ◽  
Cellular Neural Networks ◽  
Unique Equilibrium ◽  
Variable Delays

Global exponential stability is considered for a class of discrete-time cellular neural networks with variable delays. By employing a discrete Halanay inequality, a new result is presented ensuring global exponential stability of the unique equilibrium point of the networks. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the delay. An example is given to illustrate the effectiveness of the global exponential stability condition provided here.

EXPONENTIAL STABILITY ANALYSIS OF NEURAL NETWORKS WITH VARIABLE DELAYS

2010 ◽  
Vol 20 (05) ◽  
pp. 1541-1549 ◽  
Author(s):  
MAN-CHUN TAN ◽  
YAN ZHANG ◽  
WEN-LI SU ◽  
YU-NONG ZHANG
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Variable Delays

Some sufficient conditions to ensure the existence, uniqueness and global exponential stability of the equilibrium point of cellular neural networks with variable delays are derived. These results extend and improve the existing ones in the literature. Two illustrative examples are given to demonstrate the effectiveness of our results.

scholarly journals Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses

2009 ◽  
Vol 43 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Sannay Mohamad ◽  
Haydar Akça ◽  
Valéry Covachev
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Continuous Time ◽  
Global Exponential Stability ◽  
Exponential Convergence ◽  
Unique Equilibrium ◽  
Transmission Delays

Abstract A discrete-time analogue is formulated for an impulsive Cohen- -Grossberg neural network with transmission delay in a manner in which the global exponential stability characterisitics of a unique equilibrium point of the network are preserved. The formulation is based on extending the existing semidiscretization method that has been implemented for computer simulations of neural networks with linear stabilizing feedback terms. The exponential convergence in the p-norm of the analogue towards the unique equilibrium point is analysed by exploiting an appropriate Lyapunov sequence and properties of an M-matrix. The main result yields a Lyapunov exponent that involves the magnitude and frequency of the impulses. One can use the result for deriving the exponential stability of non-impulsive discrete-time neural networks, and also for simulating the exponential stability of impulsive and non-impulsive continuous-time networks.

scholarly journals On Global Exponential Stability of Discrete-Time Hopfield Neural Networks with Variable Delays

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Qiang Zhang ◽  
Xiaopeng Wei ◽  
Jin Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Stability Result ◽  
Hopfield Neural Networks ◽  
Difference Inequality ◽  
Variable Delays

Global exponential stability of a class of discrete-time Hopfield neural networks with variable delays is considered. By making use of a difference inequality, a new global exponential stability result is provided. The result only requires the delay to be bounded. For this reason, the result is milder than those presented in the earlier references. Furthermore, two examples are given to show the efficiency of our result.

DESTABILIZING EFFECTS OF IMPULSE IN DELAYED BAM NEURAL NETWORKS

2009 ◽  
Vol 23 (29) ◽  
pp. 3503-3513 ◽  
Author(s):  
CHUANDONG LI ◽  
CHAOJIE LI ◽  
CHAO LIU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Associative Memory ◽  
Global Exponential Stability ◽  
Dynamical Property ◽  
Bam Neural Networks ◽  
Bidirectional Associative Memory

This paper further studies the global exponential stability of the equilibrium point of the delayed bidirectional associative memory (DBAM) neural networks with impulse effects. Several results characterizing the aggregated effects of impulse and dynamical property of the impulse-free DBAM on the exponential stability of the considered DBAM have been established. It is shown that the impulsive DBAM will preserve the global exponential stability of the impulse-free DBAM even if the impulses have enlarging effects on the states of neurons.

A New Criterion for the Global Exponential Stability of Neural Networks with Time Delays

2013 ◽  
Vol 278-280 ◽  
pp. 1353-1358
Author(s):  
Kai Mao ◽  
Bao Shi
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Time Delays ◽  
Global Exponential Stability ◽  
Sufficient Condition ◽  
The Neural Networks ◽  
Homeomorphism Theory ◽  
New Criterion

In this paper, we study the neural networks with time delays. By using of the Homeomorphism theory and employing an inequality, constructing a new Lyapunov-Krasovskill functional, we give a new sufficient condition, which is independent of the delays, guarantying the existence, uniqueness of the equilibrium point and it’s global exponential stable. Meanwhile, the incorrectness of calculation in the previous Refs is pointed out. We therefore improve the previous results.

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