scholarly journals Global Convergence and Asymptotic Stability of Asymmetric Hopfield Neural Networks

1995 ◽  
Vol 191 (3) ◽  
pp. 405-427 ◽  
Author(s):  
Z.B. Xu ◽  
C.P. Kwong
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Convergence ◽  
Hopfield Neural Networks

ASYMPTOTIC STABILITY OF DELAY-DIFFERENCE SYSTEM OF HOPFIELD NEURAL NETWORKS VIA MATRIX INEQUALITIES AND APPLICATION

2007 ◽  
Vol 17 (05) ◽  
pp. 425-430 ◽  
Author(s):  
KREANGKRI RATCHAGIT
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Zero Solution ◽  
Hopfield Neural Networks ◽  
Discrete Version ◽  
Multiple Delays ◽  
Difference System ◽  
Matrix Inequalities ◽  
Delay Difference ◽  
Delay Difference System

In this paper, we derive a sufficient condition for asymptotic stability of the zero solution of delay-difference system of Hopfield neural networks in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method. The result is applied to obtain new asymptotic stability condition for some class of delay-difference system such as delay-difference system of Hopfield neural networks with multiple delays in terms of certain matrix inequalities. Our results can be well suited for computational purposes.

Stability for Hopfield Neural Networks With Time Delay

2002 ◽  
Vol 8 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Linshan Wang ◽  
Daoyi Xu
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Equilibrium Point ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Hopfield Neural Networks ◽  
Unique Equilibrium ◽  
Transmission Delays

In this paper, the global asymptotic stability of the equilibrium point of Hopfield neural networks with interneuronal transmission delays is studied. Some sufficient conditions related to the existence of a unique equilibrium point and its global asymptotic stability are derived.

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