Delay-dependent exponential stability for a class of neural networks with time delays and reaction–diffusion terms

2009 ◽  
Vol 346 (4) ◽  
pp. 301-314 ◽  
Author(s):  
Jianlong Qiu ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Time Delays ◽  
Reaction Diffusion ◽  
Delay Dependent

GLOBAL EXPONENTIAL STABILITY AND PERIODIC OSCILLATIONS OF REACTION–DIFFUSION BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS AND GENERAL DELAYS

2007 ◽  
Vol 17 (01) ◽  
pp. 129-142 ◽  
Author(s):  
QINGHUA ZHOU ◽  
JIANHUA SUN ◽  
GUANRONG CHEN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Activation Functions ◽  
Bidirectional Associative Memory ◽  
Connection Weight ◽  
Periodic Coefficients ◽  
Delay Dependent

For a large class of reaction–diffusion bidirectional associative memory (RDBAM) neural networks with periodic coefficients and general delays, several new delay-dependent or delay-independent sufficient conditions ensuring the existence and global exponential stability of a unique periodic solution are given, by constructing suitable Lyapunov functionals and employing some analytic techniques such as Poincaré mapping. The presented conditions are easily verifiable and useful in the design and applications of RDBAM neural networks. Moreover, the employed analytic techniques do not require the symmetry of the bidirectional connection weight matrix, the boundedness, monotonicity and differentiability of activation functions of the network. In several ways, the results generalize and improve those established in the current literature.

EXPONENTIAL STABILITY OF REACTION–DIFFUSION FUZZY RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (09) ◽  
pp. 3099-3108 ◽  
Author(s):  
QINGHUA ZHOU ◽  
LI WAN ◽  
JIANHUA SUN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Matrix Properties ◽  
Inequality Technique ◽  
Delay Dependent ◽  
Theoretical Results

Exponential stability of reaction–diffusion fuzzy recurrent neural networks (RDFRNNs) with time-varying delays are considered. By using the method of variational parameters, M-matrix properties and inequality technique, some delay-independent or delay-dependent sufficient conditions for guaranteeing the exponential stability of an equilibrium solution are obtained. One example is given to demonstrate the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document