scholarly journals Global Asymptotic Stability of Impulsive CNNs with Proportional Delays and Partially Lipschitz Activation Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xueli Song ◽  
Jigen Peng
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Asymptotic Stability ◽  
Cellular Neural Networks ◽  
Variable Coefficients ◽  
Activation Functions ◽  
Proportional Delays ◽  
Nonlinear Measure

This paper researches global asymptotic stability of impulsive cellular neural networks with proportional delays and partially Lipschitz activation functions. Firstly, by means of the transformation vi(t)=ui(et), the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Secondly, we provide novel criteria for the uniqueness and exponential stability of the equilibrium point of the latter by relative nonlinear measure and prove that the exponential stability of equilibrium point of the latter implies the asymptotic stability of one of the former. We furthermore obtain a sufficient condition to the uniqueness and global asymptotic stability of the equilibrium point of the former. Our method does not require conventional assumptions on global Lipschitz continuity, boundedness, and monotonicity of activation functions. Our results are generalizations and improvements of some existing ones. Finally, an example and its simulations are provided to illustrate the correctness of our analysis.

scholarly journals Global stability of Hopfield neural networks under dynamical thresholds with distributed delays

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
Fei-Yu Zhang ◽  
Hai-Feng Huo
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Equilibrium Point ◽  
Global Asymptotic Stability ◽  
Dynamical Behavior ◽  
Hopfield Neural Networks ◽  
Distributed Delays ◽  
Connection Matrix ◽  
Activation Functions ◽  
New Criteria

We study the dynamical behavior of a class of Hopfield neural networks with distributed delays under dynamical thresholds. Some new criteria ensuring the existence, uniqueness, and global asymptotic stability of equilibrium point are derived. In the results, we do not require the activation functions to satisfy the Lipschitz condition, and also not to be bounded, differentiable, or monotone nondecreasing. Moreover, the symmetry of the connection matrix is not also necessary. Thus, our results improve some previous works in the literature. These conditions have great importance in designs and applications of the global asymptotic stability for Hopfield neural networks involving distributed delays under dynamical thresholds.

ATTRACTABILITY AND LOCATION OF EQUILIBRIUM POINT OF CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

2004 ◽  
Vol 14 (05) ◽  
pp. 337-345 ◽  
Author(s):  
ZHIGANG ZENG ◽  
DE-SHUANG HUANG ◽  
ZENGFU WANG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Cellular Neural Networks ◽  
Stability Conditions ◽  
Time Varying ◽  
The Stability ◽  
Theoretical Results

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

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.

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