GLOBAL EXPONENTIAL STABILITY OF REACTION-DIFFUSION TIME-VARYING DELAYED CELLULAR NEURAL NETWORKS WITH DIRICHLET BOUNDARY CONDITIONS

2009 ◽  
Vol 02 (03) ◽  
pp. 377-389
Author(s):  
JIANGHONG BAI ◽  
ZHIDONG TENG ◽  
HAIJUN JIANG
Keyword(s):  
Neural Networks ◽  
Boundary Conditions ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Dirichlet Boundary ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Diffusion Time ◽  
Dirichlet Boundary Conditions ◽  
Time Varying

This paper is devoted to global exponential stability of reaction-diffusion time-varying delayed cellular neural networks with Dirichlet boundary conditions. Without assuming the monotonicity and differentiability of activation functions, nor symmetry of synaptic interconnection weights, the authors present some delay independent and easily verifiable sufficient conditions to ensure the global exponential stability of the equilibrium solution by using the method of variational parameter and inequality technique. These conditions obtained have important leading significance in the designs and applications of global exponential stability for reaction-diffusion neural circuit systems with delays. Lastly, one example is given to illustrate the theoretical analysis.

scholarly journals Existence and Global Exponential Stability of Equilibrium Solution to Reaction-Diffusion Recurrent Neural Networks on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Kaihong Zhao ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Boundary Conditions ◽  
Exponential Stability ◽  
Time Scales ◽  
Recurrent Neural Networks ◽  
Global Exponential Stability ◽  
Equilibrium Solution ◽  
Dirichlet Boundary ◽  
Reaction Diffusion ◽  
Dirichlet Boundary Conditions

The existence of equilibrium solutions to reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales is proved by the topological degree theory and M-matrix method. Under some sufficient conditions, we obtain the uniqueness and global exponential stability of equilibrium solution to reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales by constructing suitable Lyapunov functional and inequality skills. One example is given to illustrate the effectiveness of our results.

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.

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