scholarly journals Globally Exponential Stability of Periodic Solutions to Impulsive Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanfu Shao ◽  
Changjin Xu ◽  
Qianhong Zhang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Periodic Solution ◽  
Numerical Analysis ◽  
Exponential Stability ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Time Varying ◽  
Globally Exponential Stability

By using Schaeffer's theorem and Lyapunov functional, sufficient conditions of the existence and globally exponential stability of positive periodic solution to an impulsive neural network with time-varying delays are established. Applications, examples, and numerical analysis are given to illustrate the effectiveness of the main results.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

scholarly journals Exponential Stability of Periodic Solution to Wilson-Cowan Networks with Time-Varying Delays on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jinxiang Cai ◽  
Zhenkun Huang ◽  
Honghua Bin
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Time Varying

We present stability analysis of delayed Wilson-Cowan networks on time scales. By applying the theory of calculus on time scales, the contraction mapping principle, and Lyapunov functional, new sufficient conditions are obtained to ensure the existence and exponential stability of periodic solution to the considered system. The obtained results are general and can be applied to discrete-time or continuous-time Wilson-Cowan networks.

NEW CRITERIA OF ALMOST PERIODIC SOLUTION FOR BAM NEURAL NETWORKS WITH DELAYS AND IMPULSIVE EFFECTS

2007 ◽  
Vol 17 (05) ◽  
pp. 395-406 ◽  
Author(s):  
JUN CHEN ◽  
BAOTONG CUI ◽  
YAN JI
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Time Varying ◽  
Almost Periodic ◽  
Inequality Technique ◽  
New Criteria

This paper presents some sufficient conditions for the existence and global exponential stability of the almost periodic solution for impulsive bi-directional associative memory neural networks with time-varying delays by using Lyapunov functional and Gronwall-Bellmans inequality technique. Comparing with known literatures, the results of this paper are new and they complement previously known 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.

IMPROVED SUFFICIENT CONDITIONS FOR GLOBAL EXPONENTIAL STABILITY OF RECURRENT NEURAL NETWORKS WITH DISTRIBUTED DELAYS

2008 ◽  
Vol 18 (07) ◽  
pp. 2029-2037
Author(s):  
WEI WU ◽  
BAO TONG CUI ◽  
ZHIGANG ZENG
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Hopfield Neural Network ◽  
Cellular Neural Network ◽  
Distributed Delays ◽  
Globally Exponential Stability ◽  
Exponentially Stable

In this paper, the globally exponential stability of recurrent neural networks with continuously distributed delays is investigated. New theoretical results are presented in the presence of external stimuli. It is shown that the recurrent neural network is globally exponentially stable, and the estimated location of the equilibrium point can be obtained. As typical representatives, the Hopfield neural network (HNN) and the cellular neural network (CNN) are examined in detail. Comparison between our results and the previous results admits the improvement of our results.

scholarly journals Existence and Stability of Periodic Solutions for Impulsive Fuzzy Cohen-Grossberg Neural Networks on Time Scales

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Qianhong Zhang ◽  
Jingzhong Liu ◽  
Yuanfu Shao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Globally Exponential Stability ◽  
Existence And Stability

Abstract By applying the method of coincidence degree and constructing a suitable Lyapunov functional, some sufficient conditions are established for the existence and globally exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen- Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

STABILITY ANALYSIS OF A CLASS OF GENERAL PERIODIC NEURAL NETWORKS WITH DELAYS AND IMPULSES

2009 ◽  
Vol 19 (05) ◽  
pp. 375-386 ◽  
Author(s):  
YONG ZHAO ◽  
YONGHUI XIA ◽  
QISHAO LU
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Periodic Solution ◽  
Stability Analysis ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Real Life ◽  
Network Systems ◽  
Globally Exponential Stability ◽  
Special Cases

Based on the inequality analysis, matrix theory and spectral theory, a class of general periodic neural networks with delays and impulses is studied. Some sufficient conditions are established for the existence and globally exponential stability of a unique periodic solution. Furthermore, the results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results.

Periodic oscillation of memristor-based recurrent neural networks with time-varying delays and leakage delays

2018 ◽  
Vol 11 (3) ◽  
pp. 342-352
Author(s):  
Changjin Xu ◽  
Peiluan Li
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Periodic Oscillation ◽  
Time Varying ◽  
Leakage Delays ◽  
Content Type

Purpose The purpose of this paper is to investigate the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays. Design/methodology/approach The differential inequality theory and some novel mathematical analysis techniques are applied. Findings A set of sufficient conditions which guarantee the existence and global exponential stability of periodic solution of involved model is derived. Practical implications It plays an important role in designing the neural networks. Originality/value The obtained results of this paper are new and complement some previous studies. The innovation of this paper concludes two aspects: the analysis on the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays is first proposed; and it is first time to establish the sufficient criterion which ensures the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays.

scholarly journals Stability of Almost Periodic Solution for a General Class of Discontinuous Neural Networks with Mixed Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yingwei Li
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Linear Matrix ◽  
Time Varying ◽  
Almost Periodic ◽  
The Neural Networks

The global exponential stability issues are considered for almost periodic solution of the neural networks with mixed time-varying delays and discontinuous neuron activations. Some sufficient conditions for the existence, uniqueness, and global exponential stability of almost periodic solution are achieved in terms of certain linear matrix inequalities (LMIs), by applying differential inclusions theory, matrix inequality analysis technique, and generalized Lyapunov functional approach. In addition, the existence and asymptotically almost periodic behavior of the solution of the neural networks are also investigated under the framework of the solution in the sense of Filippov. Two simulation examples are given to illustrate the validity of the theoretical results.

scholarly journals Dynamics of Almost Periodic BAM Neural Networks with Neutral Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yaqin Li
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Almost Periodic

The paper investigates the almost periodic oscillatory properties of neutral-type BAM neural networks with time-varying delays. By employing the contracting mapping principle and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence, uniqueness, and global exponential stability of almost periodic solution of the system. The results of this paper are new and a simple example is given to illustrate the effectiveness of the new results.

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