ON THE GLOBAL ASYMPTOTIC STABILITY ANALYSIS OF DELAYED NEURAL NETWORKS

2005 ◽  
Vol 15 (12) ◽  
pp. 4019-4025 ◽  
Author(s):  
ZHAOHUI YUAN ◽  
DEWEN HU ◽  
LIHONG HUANG ◽  
GUOHUA DONG
Keyword(s):  
Neural Network ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Hopfield Neural Network ◽  
Cellular Neural Network ◽  
Functional Method ◽  
Activation Functions ◽  
Delayed Neural Networks ◽  
System Parameters ◽  
Lyapunov Functional Method

In this paper, the problem of the global asymptotic stability (GAS) of a class of delayed neural network is investigated. Under the generalization of dropping the boundedness and differentiability hypotheses for activation functions, using some existing results for the existence and uniqueness of the equilibrium point, we obtain a couple of general results concerning GAS by means of Lyapunov functional method without the assumption of symmetry of interconnection matrix. Our results improve and extend some previous works of other researchers. Moreover, our conditions are presented in terms of system parameters, which have leading significance in designs and applications of GAS for Hopfield neural network (HNNs) and delayed cellular neural network (DCNNs).

scholarly journals Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Xiaohong Zhang ◽  
Jianwen Jia ◽  
Xinyu Song
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Malaria Transmission ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Analytical Techniques ◽  
Functional Method ◽  
Transmission Model ◽  
Distributed Time Delay ◽  
Lyapunov Functional Method

We study the permanence, extinction, and global asymptotic stability for a nonautonomous malaria transmission model with distributed time delay. We establish some sufficient conditions on the permanence and extinction of the disease by using inequality analytical techniques. By a Lyapunov functional method, we also obtain some sufficient conditions for global asymptotic stability of this model. A numerical analysis is given to explain the analytical findings.

scholarly journals Analysis of a delay nonautonomous predator-prey system with disease in the prey

2010 ◽  
Vol 15 (1) ◽  
pp. 97-108 ◽  
Author(s):  
G. P. Samanta
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Policy Makers ◽  
Predator Prey ◽  
Analytical Technique ◽  
Predator Prey Model ◽  
Lyapunov Functional Method

In this paper we have considered a nonautonomous predator-prey model with time delay due to gestation, in which a disease that can be transmitted by contact spreads among the prey only. Here, we have established some sufficient conditions on the permanence of the system by using inequality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness.

SYNCHRONIZATION CONTROL OF NEURAL NETWORKS SUBJECT TO TIME-VARYING DELAYS AND INPUT NONLINEARITY

2006 ◽  
Vol 16 (12) ◽  
pp. 3643-3654 ◽  
Author(s):  
JUN-JUH YAN ◽  
TEH-LU LIAO ◽  
JUI-SHENG LIN ◽  
CHAO-JUNG CHENG
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Variable Structure ◽  
Hopfield Neural Network ◽  
Cellular Neural Network ◽  
Control Technique ◽  
Time Varying ◽  
Input Nonlinearity ◽  
Structure Control ◽  
Synchronization Problem

This paper investigates the synchronization problem for a particular class of neural networks subject to time-varying delays and input nonlinearity. Using the variable structure control technique, a memoryless decentralized control law is established which guarantees exponential synchronization even when input nonlinearity is present. The proposed controller is suitable for application in delayed cellular neural networks and Hopfield neural networks with no restriction on the derivative of the time-varying delays. A two-dimensional cellular neural network and a four-dimensional Hopfield neural network, both with time-varying delays, are presented as illustrative examples to demonstrate the effectiveness of the proposed synchronization scheme.

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