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 Exponential stability of impulsive neutral stochastic integrodifferential equations driven by a poisson jumps and time-varying delays

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1809-1819
Author(s):  
A. Anguraj ◽  
K. Ravikumar ◽  
E.M. Elsayed
Keyword(s):  
Fixed Point ◽  
Exponential Stability ◽  
Mild Solution ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Integrodifferential Equations ◽  
Time Varying ◽  
Mean Square ◽  
Resolvent Operators ◽  
Poisson Jumps

The purpose of this work is to study the impulsive neutral stochastic integrodifferential equations driven by a Poisson jumps and time-varying delays. We use the theory of resolvent operators developed in Grimmer the prove an existence, uniqueness and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point theory. Finally, an illustrative example is given to demonstrate the effectiveness of the results.

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.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

scholarly journals Stability of Impulsive Neural Networks with Time-Varying and Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qi Luo ◽  
Xinjie Miao ◽  
Qian Wei ◽  
Zhengxin Zhou
Keyword(s):  
Neural Networks ◽  
Existence And Uniqueness ◽  
Global Exponential Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Distributed Delays ◽  
Time Varying ◽  
Trivial Equilibrium ◽  
The Stability

This work is devoted to investigating the stability of impulsive cellular neural networks with time-varying and distributed delays. We use the new method of fixed point theory to obtain some new and concise sufficient conditions to ensure the existence and uniqueness of solution and the global exponential stability of trivial equilibrium. The presented algebraic criteria are easily checked and do not require the differentiability of delays.

scholarly journals Robust Exponential Stability of Impulsive Stochastic Neural Networks with Leakage Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chunge Lu ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Lyapunov Functions ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Mean Square ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

This paper investigates mean-square robust exponential stability of the equilibrium point of stochastic neural networks with leakage time-varying delays and impulsive perturbations. By using Lyapunov functions and Razumikhin techniques, some easy-to-test criteria of the stability are derived. Two examples are provided to illustrate the efficiency of the results.

Sign in / Sign up

Export Citation Format

Share Document