scholarly journals Stability and Passivity of Spatially and Temporally Complex Dynamical Networks with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shun-Yan Ren ◽  
Yue-Hui Zhao
Keyword(s):  
Exponential Stability ◽  
Numerical Simulations ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Functional Method ◽  
Time Varying ◽  
Complex Dynamical Network ◽  
Input And Output ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

This paper proposes a new complex dynamical network model, in which the state, input, and output variables are varied with the time and space variables. By utilizing the Lyapunov functional method combined with the inequality techniques, several criteria for passivity and global exponential stability are established. Finally, numerical simulations are given to illustrate the effectiveness of the obtained results.

Stability Analysis of Static Neural Network with Time-Varying Delays

2014 ◽  
Vol 644-650 ◽  
pp. 2442-2445
Author(s):  
Rui Zhang ◽  
Meng Xin Li ◽  
Mei Ju Liu
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Main Condition ◽  
Change Rate ◽  
Lyapunov Functional Method

In this paper, the global exponential stability is discussed for static neural networks with time varying delays. On the basis of the linear matrix inequalities (LMIs) technique, and Lyapunov functional method, we have obtained the main condition to ensure the global exponential stability of the equilibrium point for this system, which is dependent on the change rate of time varying delays. The proposed result is less restrictive than those given in the earlier literatures, easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained results, and the simulation examples are used to demonstrate the effectiveness of our results.

scholarly journals Periodic Solution for Impulsive Cellar Neural Networks with Time-Varying Delays in the Leakage Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Bingwen Liu ◽  
Shuhua Gong
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Differential Inequality ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
Activation Functions ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

This paper is concerned with impulsive cellular neural networks with time-varying delays in leakage terms. Without assuming bounded and monotone conditions on activation functions, we establish sufficient conditions on existence and exponential stability of periodic solutions by using Lyapunov functional method and differential inequality techniques. Our results are complement to some recent ones.

scholarly journals Global Exponential Stability of Almost Periodic Solutions for SICNNs with Continuously Distributed Leakage Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Hong Zhang ◽  
Mingquan Yang
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

Shunting inhibitory cellular neural networks (SICNNs) are considered with the introduction of continuously distributed delays in the leakage (or forgetting) terms. By using the Lyapunov functional method and differential inequality techniques, some sufficient conditions for the existence and exponential stability of almost periodic solutions are established. Our results complement with some recent ones.

scholarly journals Global Exponential Stability of Learning-Based Fuzzy Networks on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Juan Chen ◽  
Zhenkun Huang ◽  
Jinxiang Cai
Keyword(s):  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Fuzzy Neural Networks ◽  
New Learning ◽  
Fuzzy Neural ◽  
Lyapunov Functional Method

We investigate a class of fuzzy neural networks with Hebbian-type unsupervised learning on time scales. By using Lyapunov functional method, some new sufficient conditions are derived to ensure learning dynamics and exponential stability of fuzzy networks on time scales. Our results are general and can include continuous-time learning-based fuzzy networks and corresponding discrete-time analogues. Moreover, our results reveal some new learning behavior of fuzzy synapses on time scales which are seldom discussed in the literature.

scholarly journals Existence and Global Exponential Stability of Almost Periodic Solutions for SICNNs with Nonlinear Behaved Functions and Mixed Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Xinsong Yang ◽  
Jinde Cao ◽  
Chuangxia Huang ◽  
Yao Long
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Mixed Delays ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Inequality Techniques

By using the Leray-Schauder fixed point theorem and differential inequality techniques, several new sufficient conditions are obtained for the existence and global exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with discrete and distributed delays. The model in this paper possesses two characters: nonlinear behaved functions and all coefficients are time varying. Hence, our model is general and applicable to many known models. Moreover, our main results are also general and can be easily deduced to many simple cases, including some existing results. An example and its simulation are employed to illustrate our feasible 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.

scholarly journals A Novel Stability Analysis of Uncertain Switched Systems with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ganji Huang ◽  
Shixian Luo ◽  
Linna Wei ◽  
Wuhua Chen
Keyword(s):  
Switched Systems ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
System Parameters ◽  
Time Varying Delay ◽  
Lyapunov Functional Method ◽  
The Stability ◽  
Varying Delay

This paper deals with the stability of switched systems with time-varying delay. The time-varying system parameters are assumed to be norm-bounded. Based on a novel switched time-varying Lyapunov functional method, some new LMI-based sufficient conditions have been obtained to ensure the exponential stability for the uncertain switched delays systems. Finally, the proposed method is applied to a numerical example and the simulative results are also given.

scholarly journals Existence and Global Exponential Stability of Periodic Solutions for General Neural Networks with Time-Varying Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Xinsong Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Time Varying ◽  
Inequality Techniques ◽  
Coincidence Degree Theorem

By using the coincidence degree theorem and differential inequality techniques, sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general neural networks with time-varying (including bounded and unbounded) delays. Some known results are improved and some new results are obtained. An example is employed to illustrate our feasible results.

scholarly journals Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
G. Rajchakit ◽  
R. Sriraman ◽  
N. Boonsatit ◽  
P. Hammachukiattikul ◽  
C. P. Lim ◽  
...  
Keyword(s):  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Time Varying ◽  
Special Cases ◽  
Inequality Techniques ◽  
Complex Valued ◽  
Clifford Numbers

AbstractIn this study, we investigate the global exponential stability of Clifford-valued neural network (NN) models with impulsive effects and time-varying delays. By taking impulsive effects into consideration, we firstly establish a Clifford-valued NN model with time-varying delays. The considered model encompasses real-valued, complex-valued, and quaternion-valued NNs as special cases. In order to avoid the issue of non-commutativity of the multiplication of Clifford numbers, we divide the original n-dimensional Clifford-valued model into $2^{m}n$ 2 m n -dimensional real-valued models. Then we adopt the Lyapunov–Krasovskii functional and linear matrix inequality techniques to formulate new sufficient conditions pertaining to the global exponential stability of the considered NN model. Through numerical simulation, we show the applicability of the results, along with the associated analysis and discussion.

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