scholarly journals Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Leakage Term ◽  
Interval Neural Networks ◽  
Global Exponential Robust Stability ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

scholarly journals Attracting and Quasi-Invariant Sets of Cohen-Grossberg Neural Networks with Time Delay in the Leakage Term under Impulsive Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Differential Inequality ◽  
Invariant Sets ◽  
Leakage Term ◽  
Impulsive Perturbations ◽  
Delay Differential ◽  
Delay Differential Inequality

A class of impulsive Cohen-Grossberg neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, the attracting and invariant sets of the networks are obtained. The results in this paper extend and improve the earlier publications. An example is presented to illustrate the effectiveness of our conclusion.

GLOBAL EXPONENTIAL STABILITY CONDITIONS FOR DELAYED PARABOLIC NEURAL NETWORKS WITH VARIABLE COEFFICIENTS

2007 ◽  
Vol 17 (12) ◽  
pp. 4409-4415
Author(s):  
XUYANG LOU ◽  
BAOTONG CUI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Lyapunov Functionals ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

In this paper, we present a class of delayed parabolic neural networks (DPNN) with variable coefficients. Some sufficient conditions for the global exponential stability of the DPNN with variable coefficients are derived by a method based on delay differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of DPNN with variable coefficients.

scholarly journals A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Baltazar Aguirre-Hernández ◽  
Raúl Villafuerte-Segura ◽  
Alberto Luviano-Juárez ◽  
Carlos Arturo Loredo-Villalobos ◽  
Edgar Cristian Díaz-González
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Dynamical Systems ◽  
The Stability ◽  
Numerical Approaches

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

scholarly journals Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Mingzhu Song ◽  
Quanxin Zhu ◽  
Hongwei Zhou
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Stochastic Neural Networks ◽  
Stochastic Delay Differential Equations ◽  
Almost Sure Stability ◽  
Infinitesimal Operator ◽  
Lasalle Invariant Principle ◽  
The Stability ◽  
Delay Differential

The stability issue is investigated for a class of stochastic neural networks with time delays in the leakage terms. Different from the previous literature, we are concerned with the almost sure stability. By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s formula, and stochastic analysis theory, some novel sufficient conditions are derived to guarantee the almost sure stability of the equilibrium point. In particular, the weak infinitesimal operator of Lyapunov functions in this paper is not required to be negative, which is necessary in the study of the traditional moment stability. Finally, two numerical examples and their simulations are provided to show the effectiveness of the theoretical results and demonstrate that time delays in the leakage terms do contribute to the stability of stochastic neural networks.

scholarly journals Novel Criteria on Global Robust Exponential Stability to a Class of Reaction-Diffusion Neural Networks with Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Jie Pan ◽  
Shouming Zhong
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Compact Sets ◽  
Robust Exponential Stability ◽  
Delayed Neural Networks ◽  
Global Exponential Robust Stability

The global exponential robust stability is investigated to a class of reaction-diffusion Cohen-Grossberg neural network (CGNNs) with constant time-delays, this neural network contains time invariant uncertain parameters whose values are unknown but bounded in given compact sets. By employing the Lyapunov-functional method, several new sufficient conditions are obtained to ensure the global exponential robust stability of equilibrium point for the reaction diffusion CGNN with delays. These sufficient conditions depend on the reaction-diffusion terms, which is a preeminent feature that distinguishes the present research from the previous research on delayed neural networks with reaction-diffusion. Two examples are given to show the effectiveness of the obtained results.

scholarly journals Stability of linear neutral delay-differential systems

1988 ◽  
Vol 38 (3) ◽  
pp. 339-344 ◽  
Author(s):  
Li-Ming Li
Keyword(s):  
Differential Inequality ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

Sufficient conditions are obtained for the stability of linear neutral delay-differential systems by using a delay-differential inequality.

P-Bifurcation Aspects of a Modified Duffing Oscillator Near Equilibrium

2001 ◽  
Author(s):  
M. S. Fofana ◽  
Dariusz Szwarc
Keyword(s):  
Time Delay ◽  
Averaging Method ◽  
Duffing Oscillator ◽  
Sufficient Conditions ◽  
Stability Study ◽  
Unified Framework ◽  
Positive Time ◽  
Moment Lyapunov Exponent ◽  
The Stability ◽  
Delay Differential

Abstract A unified framework for the study of stability of solutions to delay differential equations perturbed deterministically and stochastically has been presented. We review the concepts of Hopf bifurcation, centre manifold, integral averaging method and pth–moment Lyapunov exponent, and then demonstrate their role in the stability study of a modified Duffing oscillator with time delay. Sufficient conditions ensuring Đ- and Þ–bifurcations and the changes in character of the probability density function are established for fixed and positive time delay.

DELAY INDEPENDENT AND DEPENDENT STABILITY ANALYSIS FOR COHEN–GROSSBERG NEURAL NETWORKS WITH TIME-VARYING DELAYS

2009 ◽  
Vol 19 (09) ◽  
pp. 3149-3159
Author(s):  
YIGUANG LIU ◽  
ZHISHENG YOU ◽  
BINGBING LIU
Keyword(s):  
Neural Networks ◽  
Global Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Time Varying ◽  
Activation Functions ◽  
Delay Differential ◽  
Delay Dependent ◽  
Delay Differential Inequality

For Cohen–Grossberg neural networks with time-varying delays, by fixed point and contract mapping theorems, a sufficient condition ensuring the existence and uniqueness of an equilibrium is proposed. To guarantee the delay independent global stability of the equilibrium, two sufficient conditions are proposed by means of a time delay differential inequality and contradiction tricks, respectively. By virtue of a special Lyapunov functional as well as properties of M-matrices, a sufficient condition undertaking the delay dependent global stability of the equilibrium is introduced. Compared with known literatures, the presented results place slack restrictions on the activation functions, and are suitable for the networks with time-varying delays. Furthermore, most of the obtained results are independent of the amplification functions, making their applicability more far-reaching. Finally, two examples are numerically simulated to illustrate the validity as well as novelty of the criteria.

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