scholarly journals Exponential Stability for Impulsive Stochastic Nonlinear Network Systems with Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Lanping Chen ◽  
Zhengzhi Han ◽  
Zhenghua Ma
Keyword(s):  
Numerical Simulation ◽  
Time Delay ◽  
Exponential Stability ◽  
Nonlinear Equations ◽  
Sufficient Conditions ◽  
Impulsive Systems ◽  
Complex Dynamical Network ◽  
Network Systems ◽  
Dynamical Network ◽  
Nonlinear Network

We study the exponential stability of the complex dynamical network described by differentially nonlinear equations which couple with time delay and stochastic impulses. Some sufficient conditions are established to ensurepth moment exponential stable for the stochastic impulsive systems (SIS) with time delay. An example with its numerical simulation is presented to illustrate the validation of main results.

scholarly journals Exponential Stability of Stochastic Differential Equation with Mixed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenli Zhu ◽  
Jiexiang Huang ◽  
Xinfeng Ruan ◽  
Zhao Zhao
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Stochastic Differential Equation ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Martingale Inequality ◽  
Mixed Delay ◽  
Exponentially Stable ◽  
Theoretical Results

This paper focuses on a class of stochastic differential equations with mixed delay based on Lyapunov stability theory, Itô formula, stochastic analysis, and inequality technique. A sufficient condition for existence and uniqueness of the adapted solution to such systems is established by employing fixed point theorem. Some sufficient conditions of exponential stability and corollaries for such systems are obtained by using Lyapunov function. By utilizing Doob’s martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. In particular, our theoretical results show that if stochastic differential equation is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic differential equation with mixed delay will remain exponentially stable. Moreover, time delay upper limit is solved by using our theoretical results when the system is exponentially stable, and they are more easily verified and applied in practice.

scholarly journals Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenli Zhu ◽  
Xinfeng Ruan ◽  
Ye Qin ◽  
Jie Zhuang
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Price System ◽  
Nonlinear Dynamical ◽  
System With Delay ◽  
Exponentially Stable ◽  
Theoretical Results

Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to ann-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.

Exponential Stability of Stochastic Reaction-Diffusion Neural Networks with Mixed Delays in Procurement of Maintenance Material

2011 ◽  
Vol 105-107 ◽  
pp. 2315-2320
Author(s):  
Xiao Chen
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Exponential Stability ◽  
Effective Means ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Mixed Delays ◽  
The Neural Network ◽  
Discrete Time Delay

In order to effectively improve the equipment maintenance material procurement management efficiency, improve economic efficiency of using the procurement funds, strengthen mathematical theory applications in the area of procurement, the neural network used in evaluation of organizational change is one of the most effective means. In this paper, a class of stochastic Cohen–Grossberg neural networks with reaction-diffusion terms, discrete time delay and distributed time delay is investigated. First, we describe the modeling, illuminate the significance of the system and introduce some preliminary definitions and lemmas which will be employed throughout the paper. Then, by using the Lyapunov functional method, M-matrix properties, nonnegative semimartingale convergence theorem and some inequality technique, sufficient conditions are obtained to guarantee the exponential stability of the system.

Topological Identification of Complex Dynamical Network with Communities and Node Delay

2013 ◽  
Vol 411-414 ◽  
pp. 2093-2097
Author(s):  
Jiang Ang Zhang ◽  
Yan Dong Chu ◽  
Wen Ju Du
Keyword(s):  
Parameter Identification ◽  
Hierarchical Structure ◽  
Invariance Principle ◽  
Topological Structure ◽  
Complex Dynamical Networks ◽  
Complex Dynamical Network ◽  
Network Systems ◽  
Dynamical Network ◽  
General Complex ◽  
Real Complex

Recently, various papers investigated the topology identification and parameter identification of uncertain general complex dynamical networks. However, in many real complex dynamical network systems, there exists community or hierarchical structure and node delay. Based on LaSalle’s invariance principle, in this letter, an adaptive controlling method is proposed to identify unknown topological structure for general weighted complex dynamical network with community and node delay. Illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme.

scholarly journals Input-to-State Stability for Dynamical Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Weisong Zhou ◽  
Zhichun Yang
Keyword(s):  
Sufficient Conditions ◽  
Network Models ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Neural Network Models ◽  
Network Systems ◽  
Nonlinear Network ◽  
Dynamical Neural Network ◽  
Dynamical Neural Networks

A class of dynamical neural network models with time-varying delays is considered. By employing the Lyapunov-Krasovskii functional method and linear matrix inequalities (LMIs) technique, some new sufficient conditions ensuring the input-to-state stability (ISS) property of the nonlinear network systems are obtained. Finally, numerical examples are provided to illustrate the efficiency of the derived results.

Comparison principle for difference equations with variable-time impulses

2018 ◽  
Vol 32 (02) ◽  
pp. 1850013
Author(s):  
Hongfei Li ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Exponential Stability ◽  
Comparison Principle ◽  
Difference Equations ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Fixed Time ◽  
Impulsive Systems ◽  
Comparison System ◽  
Variable Time ◽  
The Difference

In this paper, a class of difference equations with variable-time impulses is considered. By applying comparison principle, we shall show that difference equations with variable-time impulse can be reduced to the corresponding difference equations with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the difference equations with variable-time impulses. Furthermore, we use a series of sufficient criteria to illustrate the same stability properties between variable-time impulsive difference equations and the fixed-time ones. We then establish several sufficient conditions guaranteeing the global exponential stability of variable-time impulsive difference equations by comparison principle. As an application, global exponential stability of discrete-time neural networks with variable-time impulses is discussed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.

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