scholarly journals Global exponential stability of impulsive cellular neural networks with time-varying delays via fixed point theory

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Yutian Zhang ◽  
Qi Luo
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cellular Neural Networks ◽  
Time Varying

scholarly journals Mean-Square Exponential Stability Analysis of Stochastic Neural Networks with Time-Varying Delays via Fixed Point Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Tianxiang Yao ◽  
Xianghong Lai
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Exponential Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Stability Study ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Mean Square

This work addresses the stability study for stochastic cellular neural networks with time-varying delays. By utilizing the new research technique of the fixed point theory, we find some new and concise sufficient conditions ensuring the existence and uniqueness as well as mean-square global exponential stability of the solution. The presented algebraic stability criteria are easily checked and do not require the differentiability of delays. The paper is finally ended with an example to show the effectiveness of the obtained results.

scholarly journals Fixed Point and Asymptotic Analysis of Cellular Neural Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Xianghong Lai ◽  
Yutian Zhang
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Trivial Equilibrium ◽  
The Stability

We firstly employ the fixed point theory to study the stability of cellular neural networks without delays and with time-varying delays. Some novel and concise sufficient conditions are given to ensure the existence and uniqueness of solution and the asymptotic stability of trivial equilibrium at the same time. Moreover, these conditions are easily checked and do not require the differentiability of delays.

scholarly journals Global Exponential Stability and Periodicity of Nonautonomous Impulsive Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Weiyi Hu ◽  
Kelin Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Point Theory ◽  
Time Varying ◽  
Nonautonomous Systems ◽  
Inequality Techniques

In this paper, we investigate the global exponential stability and periodicity of nonautonomous cellular neural networks with reaction-diffusion, impulses, and time-varying delays. By establishing a new differential inequality for nonautonomous systems, using the properties of M-matrix and inequality techniques, some new sufficient conditions for the global exponential stability of the system are obtained. Moreover, sufficient conditions for the periodic solutions of the system are obtained by using the Poincare mapping and the fixed point theory. The validity and superiority of the main results are verified by numerical examples and simulations.

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.

scholarly journals Anti-Periodic Dynamics of Quaternion-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays on Time Scales

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Shiping Shen ◽  
Bing Li ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Global Exponential Stability ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Analysis Techniques ◽  
Periodic Dynamics

A class of quaternion-valued fuzzy cellular neural networks with time-varying delays on time scales is proposed. Based on inequality analysis techniques on time scales, a fixed point theorem and the theory of calculus on time scales, the existence, and global exponential stability of anti-periodic solutions for this class of neural networks are established. The obtained results are completely new and supplement to the known results. Finally, a numerical example is given to illustrate the feasibility of our results.

Sign in / Sign up

Export Citation Format

Share Document