Global exponential stability of interval general BAM neural networks with reaction–diffusion terms and multiple time-varying delays

2011 ◽  
Vol 24 (5) ◽  
pp. 457-465 ◽  
Author(s):  
Zhengqiu Zhang ◽  
Yan Yang ◽  
Yesheng Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Reaction Diffusion ◽  
Multiple Time ◽  
Time Varying ◽  
Bam Neural Networks

scholarly journals Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Kaiyu Liu ◽  
Zhengqiu Zhang ◽  
Liping Wang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Degree Theory ◽  
Multiple Time ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Lipschitz Continuous ◽  
Sign Conditions

We investigate first the existence of periodic solution in general Cohen-Grossberg BAM neural networks with multiple time-varying delays by means of using degree theory. Then using the existence result of periodic solution and constructing a Lyapunov functional, we discuss global exponential stability of periodic solution for the above neural networks. Our result on global exponential stability of periodic solution is different from the existing results. In our result, the hypothesis for monotonicity ineqiality conditions in the works of Xia (2010) Chen and Cao (2007) on the behaved functions is removed and the assumption for boundedness in the works of Zhang et al. (2011) and Li et al. (2009) is also removed. We just require that the behaved functions satisfy sign conditions and activation functions are globally Lipschitz continuous.

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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