An analysis of global exponential stability of neural networks with reaction-diffusion terms and distributed delays

2010 ◽  
Vol 2 (4) ◽  
pp. 401
Author(s):  
Zhenjiang Zhao ◽  
Deqian Xue ◽  
Qiankun Song
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Reaction Diffusion ◽  
Distributed Delays

NEW CRITERIA ON GLOBAL EXPONENTIAL STABILITY OF BAM NEURAL NETWORKS WITH DISTRIBUTED DELAYS AND REACTION-DIFFUSION TERMS

2007 ◽  
Vol 17 (01) ◽  
pp. 43-52 ◽  
Author(s):  
XUYANG LOU ◽  
BAOTONG CUI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Reaction Diffusion ◽  
Kernel Functions ◽  
Distributed Delays ◽  
Analysis Technique ◽  
Inequality Technique ◽  
New Criteria ◽  
Theoretical Results

This paper presents new theoretical results on global exponential stability of bi-directional associative memory neural networks with distributed delays and reaction-diffusion terms based on the inequality technique, Lyapunov functional, and analysis technique. The results remove the usual assumption that the activation functions are of monotonous or differential character. Exponential converging velocity index is estimated, which depends on the delay kernel functions and system parameters. Finally, two numerical examples are given to show the validity and feasibility of our results.

scholarly journals Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Quan Xu ◽  
Zilong Chen ◽  
Weifan Zheng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Time Varying ◽  
Homeomorphism Mapping ◽  
Complex Valued

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.

Sign in / Sign up

Export Citation Format

Share Document