scholarly journals Exponential Stability and Numerical Methods of Stochastic Recurrent Neural Networks with Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Shifang Kuang ◽  
Yunjian Peng ◽  
Feiqi Deng ◽  
Wenhua Gao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Mean Square ◽  
Stochastic Delay ◽  
Backward Euler ◽  
Inequality Techniques ◽  
The Stability ◽  
Stability In Mean Square

Exponential stability in mean square of stochastic delay recurrent neural networks is investigated in detail. By using Itô’s formula and inequality techniques, the sufficient conditions to guarantee the exponential stability in mean square of an equilibrium are given. Under the conditions which guarantee the stability of the analytical solution, the Euler-Maruyama scheme and the split-step backward Euler scheme are proved to be mean-square stable. At last, an example is given to demonstrate our results.

scholarly journals Existence, Uniqueness, and Exponential Stability of Uncertain Delayed Neural Networks with Inertial Term: Nonreduced Order Case

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
M. Iswarya ◽  
R. Raja ◽  
Q. Zhu ◽  
M. Niezabitowski ◽  
J. Alzabut ◽  
...  
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Inertial Term ◽  
Delayed Neural Networks ◽  
Neural Network System ◽  
Inertial Neural Networks ◽  
Inequality Techniques ◽  
The Stability ◽  
Necessary And Sufficient

In this work, we mainly focus on uncertain delayed neural network system with inertial term. Here, the existence, uniqueness, and exponential stability of inertial neural networks are derived without shifting the second order differential system into first order through substituting variables. Initially, we construct a proper Lyapunov–Krasovskii functional to investigate the stability of novel uncertain delayed inertial neural networks, which is different from the classical Lyapunov functional approach. By utilizing the Kirchhoff’s matrix tree theorem, Cauchy–Schwartz inequality, homeomorphism theorem, and some inequality techniques, the necessary and sufficient conditions are derived for the designed framework. Subsequently, to exhibit the strength of this outcome, we framed a quantitative example.

ALMOST SURE EXPONENTIAL STABILITY OF STOCHASTIC RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2010 ◽  
Vol 20 (02) ◽  
pp. 539-544 ◽  
Author(s):  
LI WAN ◽  
QINGHUA ZHOU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Almost Sure Exponential Stability ◽  
The Stability

The stability of stochastic recurrent neural networks with time-varying delays is investigated. A set of novel sufficient conditions on almost sure exponential stability has been established. Two examples are also given to illustrate the effectiveness of our results.

scholarly journals Mean Square Exponential Stability of Stochastic Cohen-Grossberg Neural Networks with Unbounded Distributed Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Chuangxia Huang ◽  
Lehua Huang ◽  
Yigang He
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Mean Square ◽  
State Variables ◽  
Analysis Technique ◽  
Mean Square Exponential Stability ◽  
Unbounded Distributed Delays ◽  
Inequality Techniques

This paper addresses the issue of mean square exponential stability of stochastic Cohen-Grossberg neural networks (SCGNN), whose state variables are described by stochastic nonlinear integrodifferential equations. With the help of Lyapunov function, stochastic analysis technique, and inequality techniques, some novel sufficient conditions on mean square exponential stability for SCGNN are given. Furthermore, we also establish some sufficient conditions for checking exponential stability for Cohen-Grossberg neural networks with unbounded distributed delays.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

scholarly journals A perspective on graph theory-based stability analysis of impulsive stochastic recurrent neural networks with time-varying delays

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
M. Iswarya ◽  
R. Raja ◽  
G. Rajchakit ◽  
J. Cao ◽  
J. Alzabut ◽  
...  
Keyword(s):  
Neural Networks ◽  
Graph Theory ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Lyapunov Functional ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Theoretic Approach ◽  
Discrete Time Delay

AbstractIn this work, the exponential stability problem of impulsive recurrent neural networks is investigated; discrete time delay, continuously distributed delay and stochastic noise are simultaneously taken into consideration. In order to guarantee the exponential stability of our considered recurrent neural networks, two distinct types of sufficient conditions are derived on the basis of the Lyapunov functional and coefficient of our given system and also to construct a Lyapunov function for a large scale system a novel graph-theoretic approach is considered, which is derived by utilizing the Lyapunov functional as well as graph theory. In this approach a global Lyapunov functional is constructed which is more related to the topological structure of the given system. We present a numerical example and simulation figures to show the effectiveness of our proposed work.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (03) ◽  
pp. 207-218 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YONGMIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Neuron Activation ◽  
Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

ASYMPTOTIC HYPERSTABILITY OF A CLASS OF NEURAL NETWORKS

1999 ◽  
Vol 09 (02) ◽  
pp. 95-98 ◽  
Author(s):  
ANKE MEYER-BÄSE
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lyapunov Methods ◽  
Network Parameters ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Stability Results

This paper is concerned with the asymptotic hyperstability of recurrent neural networks. We derive based on the stability results necessary and sufficient conditions for the network parameters. The results we achieve are more general than those based on Lyapunov methods, since they provide milder constraints on the connection weights than the conventional results and do not suppose symmetry of the weights.

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.

EXPONENTIAL STABILITY OF STOCHASTIC FUZZY CELLULAR NEURAL NETWORKS WITH DISTRIBUTED DELAYS

2009 ◽  
Vol 19 (10) ◽  
pp. 3387-3395 ◽  
Author(s):  
LIPING CHEN ◽  
RANCHAO WU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Lyapunov Functional ◽  
Equilibrium Solution ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Distributed Delays ◽  
Fuzzy Cellular Neural Networks ◽  
Mean Square Exponential Stability ◽  
Inequality Techniques

The exponential stability of a class of stochastic fuzzy cellular neural networks with distributed delays is investigated in this paper. By using analytic methods such as Lyapunov functional, Itô's formula, inequality techniques and non-negative semimartingale convergence theorem, the sufficient conditions guaranteeing the almost sure and mean square exponential stability of its equilibrium solution are respectively obtained. For illustration, an example is given to show the feasibility of results.

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