scholarly journals Generalized Outer Synchronization of Stochastic Neural Networks With Time-Varying Delays

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Ping He
Keyword(s):  
Neural Networks ◽  
Brownian Motion ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Dynamical Networks ◽  
Outer Synchronization ◽  
Stochastic Disturbance ◽  
Stochastic Invariance

Abstract In this paper, generalized outer synchronization between two different stochastic coupled complex dynamical networks with time-varying delays has been investigated. A novel controller is given and the stochastic invariance principle is applied. A stochastic disturbance which is described in term of a Brownian motion are considered in complex dynamical networks. Moreover, some sufficient conditions are derived to ensure generalized outer synchronization of stochastic neural networks. Surprisingly, it is found that complex networks with different structure can be synchronized.

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 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 Adaptive-Impulsive Control of the Projective Synchronization in Drive-Response Complex Dynamical Networks with Time-Varying Coupling

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Song Zheng
Keyword(s):  
Impulsive Control ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Projective Synchronization ◽  
Time Varying ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Hybrid Controller ◽  
The Stability ◽  
Response Complex

This paper investigates the projective synchronization (PS) of drive-response time-varying coupling complex dynamical networks with time delay via an adaptive-impulsive controlling method, in which the weights of links are time varying. Based on the stability analysis of impulsive control system, sufficient conditions for the PS are derived, and a hybrid controller, that is, an adaptive feedback controller with impulsive control effects, is designed. Numerical simulations are performed to verify the correctness and effectiveness of theoretical result.

Ultimate Boundedness of Stochastic Neural Networks with Delays

2011 ◽  
Vol 204-210 ◽  
pp. 1549-1552
Author(s):  
Li Wan ◽  
Qing Hua Zhou
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Lyapunov Functional ◽  
Signal Transmission ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequality ◽  
Ultimate Boundedness

Although ultimate boundedness of several classes of neural networks with constant delays was studied by some researchers, the inherent randomness associated with signal transmission was not taken account into these networks. At present, few authors study ultimate boundedness of stochastic neural networks and no related papers are reported. In this paper, by using Lyapunov functional and linear matrix inequality, some sufficient conditions ensuring the ultimate boundedness of stochastic neural networks with time-varying delays are established. Our criteria are easily tested by Matlab LMI Toolbox. One example is given to demonstrate our criteria.

scholarly journals Square-Mean Pseudo Almost Periodic Solutions for Quaternion-Valued Stochastic Neural Networks with Time-Varying Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Yuanyuan Hou ◽  
Lihua Dai
Keyword(s):  
Neural Networks ◽  
Stochastic Analysis ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Almost Periodic ◽  
Analysis Techniques ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic

In this paper, we are concerned with a class of quaternion-valued stochastic neural networks with time-varying delays. Firstly, we cannot explicitly decompose the quaternion-valued stochastic systems into equivalent real-valued stochastic systems; by using the Banach fixed point theorem and stochastic analysis techniques, we obtain some sufficient conditions for the existence of square-mean pseudo almost periodic solutions for this class of neural networks. Then, by constructing an appropriate Lyapunov functional and stochastic analysis techniques, we can also obtain sufficient conditions for square-mean exponential stability of the considered neural networks. All of these results are new. Finally, two examples are given to illustrate the effectiveness and feasibility of our main results.

Mean Square Asymptotic Stability of Neutral Stochastic Neutral Networks with Multiple Time-Varying Delays

2013 ◽  
Vol 684 ◽  
pp. 579-582
Author(s):  
Xiang Dong Shi
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Neural Networks ◽  
Multiple Time ◽  
Time Varying ◽  
Lyapunov Functional Method ◽  
Inequality Techniques ◽  
Neutral Stochastic Neural Networks

The paper considers the problems of almost surely asymptotic stability for neutral stochastic neural networks with multiple time-varying delays. By applying Lyapunov functional method and differential inequality techniques, new sufficient conditions ensuring the existence and almost surely asymptotic stability of neutral stochastic neural networks with multiple time-varying delays are established. The results are shown to be generalizations of some previously published results and are less conservative than existing results.

Analyzing synchronization of time-delayed complex dynamical networks with periodic on-off coupling

2017 ◽  
Vol 31 (28) ◽  
pp. 1750210
Author(s):  
Wang Li ◽  
Yongzheng Sun ◽  
Youquan Liu ◽  
Donghua Zhao
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Sufficient Conditions ◽  
Numerical Results ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Outer Synchronization ◽  
Synchronization Time ◽  
Integer Multiple ◽  
Delay Step

We investigate the synchronization of time-delayed complex dynamical networks with periodic on-off coupling. We derive sufficient conditions for the complete and generalized outer synchronization. Both our analytical and numerical results show that two time-delayed networks can achieve outer synchronization even if the couplings between the two networks switch off periodically. This synchronization behavior is largely dependent of the coupling strength, the on-off period, the on-off rate and the time delay. In particular, we find that the synchronization time nonmonotonically increases as the time delay increases when the time delay step is not equal to an integer multiple of the on-off period.

scholarly journals Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 742 ◽  
Author(s):  
Pharunyou Chanthorn ◽  
Grienggrai Rajchakit ◽  
Jenjira Thipcha ◽  
Chanikan Emharuethai ◽  
Ramalingam Sriraman ◽  
...  
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Equivalent Representation ◽  
Stochastic Effects ◽  
Complex Valued

In practical applications, stochastic effects are normally viewed as the major sources that lead to the system’s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov–Krasovskii functional and applying Jensen’s inequality, a number of sufficient conditions can be derived by utilizing It o ^ ’s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.

scholarly journals Globalμ-Stability Analysis for Impulsive Stochastic Neural Networks with Unbounded Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Lizi Yin ◽  
Xinchun Wang
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Delays ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Software Packages ◽  
The Mean ◽  
Theoretical Results

We investigate the globalμ-stability in the mean square of impulsive stochastic neural networks with unbounded time-varying delays and continuous distributed delays. By choosing an appropriate Lyapunov-Krasovskii functional, a novel robust stability condition, in the form of linear matrix inequalities, is derived. These sufficient conditions can be tested by MATLAB LMI software packages. The results extend and improve the earlier publication. Two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

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