Employing the Friedrichs’ inequality to ensure global exponential stability of delayed reaction-diffusion neural networks with nonlinear boundary conditions

2020 ◽  
Vol 383 ◽  
pp. 81-94
Author(s):  
Puchen Liu ◽  
Guoyan Cao
Keyword(s):  
Neural Networks ◽  
Boundary Conditions ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Nonlinear Boundary ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Delayed Reaction ◽  
Friedrichs Inequality

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.

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.

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