Robustness analysis for global exponential stability of reaction diffusion neural networks in the presence of uncertainty in connection weight matrices and noise

2014 ◽  
Author(s):  
Yan Li ◽  
Junhao Hu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Robustness Analysis ◽  
Reaction Diffusion ◽  
Connection Weight

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.

scholarly journals Preserving Global Exponential Stability of Hybrid BAM Neural Networks with Reaction Diffusion Terms in the Presence of Stochastic Noise and Connection Weight Matrices Uncertainty

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yan Li ◽  
Yi Shen
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Reaction Diffusion ◽  
Stochastic Noise ◽  
Bam Neural Networks ◽  
Connection Weight ◽  
Exponentially Stable ◽  
The Neural Networks ◽  
The Impact

We study the impact of stochastic noise and connection weight matrices uncertainty on global exponential stability of hybrid BAM neural networks with reaction diffusion terms. Given globally exponentially stable hybrid BAM neural networks with reaction diffusion terms, the question to be addressed here is how much stochastic noise and connection weights matrices uncertainty the neural networks can tolerate while maintaining global exponential stability. The upper threshold of stochastic noise and connection weights matrices uncertainty is defined by using the transcendental equations. We find that the perturbed hybrid BAM neural networks with reaction diffusion terms preserve global exponential stability if the intensity of both stochastic noise and connection weights matrices uncertainty is smaller than the defined upper threshold. A numerical example is also provided to illustrate the theoretical conclusion.

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