scholarly journals Dynamical Analysis for High-Order Delayed Hopfield Neural Networks with Impulses

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Dengwang Li
Keyword(s):  
Neural Networks ◽  
Functional Method ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Dynamical Analysis ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Linear Matrix Inequality Approach ◽  
Lyapunov Functional Method

The global exponential stability and uniform stability of the equilibrium point for high-order delayed Hopfield neural networks with impulses are studied. By utilizing Lyapunov functional method, the quality of negative definite matrix, and the linear matrix inequality approach, some new stability criteria for such system are derived. The results are related to the size of delays and impulses. Two examples are also given to illustrate the effectiveness of our results.

scholarly journals LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yangfan Wang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Global Exponential Robust Stability

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

scholarly journals Global Exponential Robust Stability of High-Order Hopfield Neural Networks with S-Type Distributed Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Haiyong Zheng ◽  
Bin Wu ◽  
Tengda Wei ◽  
Linshan Wang ◽  
Yangfan Wang
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Differential Inequality ◽  
Time Delays ◽  
Functional Method ◽  
High Order ◽  
Distributed Time Delays ◽  
Inequality Technique ◽  
Global Exponential Robust Stability ◽  
Lyapunov Functional Method

By employing differential inequality technique and Lyapunov functional method, some criteria of global exponential robust stability for the high-order neural networks with S-type distributed time delays are established, which are easy to be verified with a wider adaptive scope.

scholarly journals Almost Sure Asymptotical Adaptive Synchronization for Neutral-Type Neural Networks with Stochastic Perturbation and Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Wuneng Zhou ◽  
Xueqing Yang ◽  
Jun Yang ◽  
Anding Dai ◽  
Huashan Liu
Keyword(s):  
Neural Networks ◽  
Neutral Type ◽  
Stochastic Perturbation ◽  
Adaptive Controller ◽  
Functional Method ◽  
Markovian Switching ◽  
Adaptive Synchronization ◽  
Linear Matrix ◽  
Lyapunov Functional Method ◽  
New Criterion

The problem of almost sure (a.s.) asymptotic adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching is researched. Firstly, we proposed a new criterion of a.s. asymptotic stability for a general neutral-type stochastic differential equation which extends the existing results. Secondly, based upon this stability criterion, by making use of Lyapunov functional method and designing an adaptive controller, we obtained a condition of a.s. asymptotic adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching. The synchronization condition is expressed as linear matrix inequality which can be easily solved by Matlab. Finally, we introduced a numerical example to illustrate the effectiveness of the method and result obtained in this paper.

scholarly journals Delay-Dependent Dynamics of Switched Cohen-Grossberg Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Peng Wang ◽  
Haijun Hu ◽  
Zheng Jun ◽  
Yanxiang Tan ◽  
Li Liu
Keyword(s):  
Neural Networks ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Ultimate Boundedness ◽  
Globally Exponential Stability ◽  
Lyapunov Functional Method ◽  
Uniformly Ultimate Boundedness ◽  
Delay Dependent

This paper aims at studying the problem of the dynamics of switched Cohen-Grossberg neural networks with mixed delays by using Lyapunov functional method, average dwell time (ADT) method, and linear matrix inequalities (LMIs) technique. Some conditions on the uniformly ultimate boundedness, the existence of an attractors, the globally exponential stability of the switched Cohen-Grossberg neural networks are developed. Our results extend and complement some earlier publications.

The Globally Asymptotic Stability Analysis of the Delayed Recurrent Neural Networks Stability Criterion via LMI Technique and Nonsmooth Analysis

2013 ◽  
Vol 380-384 ◽  
pp. 2030-2033
Author(s):  
Zhen Cai Li ◽  
Yang Wang
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Recurrent Neural Networks ◽  
Nonsmooth Analysis ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Globally Asymptotic Stability ◽  
Lyapunov Functional Method

This paper considers the problem of globally asymptotic stability of the recurrent neural networks with time-varying delays. A linear matrix inequality (LMI) technology and Lyapunov functional method is employed by combing the means of the nonsmooth analysis. A few new sufficient conditions and criterions were proposed to ensure the delayed recurrent neural networks are uniqueness and globally asymptotic stability of their equilibrium point. A few simulation examples are presented to demonstrate the effectiveness of the results and to improve feasibility.

Global Stability Properties for Neutral-Type Hopfield Neural Networks

2012 ◽  
Vol 232 ◽  
pp. 682-685
Author(s):  
Dao He Hao ◽  
Liang Wu
Keyword(s):  
Neural Networks ◽  
Global Stability ◽  
Neutral Type ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Functional Stability ◽  
Stability Properties ◽  
Linear Matrix Inequality Approach

The global stability properties was discussed for the neutral-type Hopfield neural networks with discrete and distributed time-varying delays .Based on the Lyapunov functional stability analysis and the linear matrix inequality approach, a new sufficient condition was derived to assure the global stability properties of the equilibrium. The criterion improved and extended the results of literature, and has less conservative.

scholarly journals Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays

2011 ◽  
Vol 21 (1) ◽  
pp. 127-135 ◽  
Author(s):  
Ramachandran Raja ◽  
Rathinasamy Sakthivel ◽  
Selvaraj Anthoni ◽  
Hyunsoo Kim
Keyword(s):  
Neural Networks ◽  
Hopfield Neural Networks ◽  
Markovian Switching ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Discrete State ◽  
Delay Dependent

Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delaysThe paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.

Mean Square Exponential Stability of Stochastic High-Order Hopfield Neural Networks with Time-Varying Delays

2013 ◽  
Vol 303-306 ◽  
pp. 1532-1535
Author(s):  
Xiang Dong Shi
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Neural System ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Mean Square ◽  
Neuron Activation ◽  
Mean Square Exponential Stability

The paper considers the problems of global exponential stability for stochastic delayed high-order Hopfield neural networks with time-varying delays. By employing the linear matrix inequality(LMI) and the Lyapunov functional methods, we present some new criteria ensuring globally mean square exponential stability. The results impose constraint conditions on the network parameters of neural system independent. The results are applicable to all continuous non-monotonic neuron activation functions.

scholarly journals New Results for Periodic Solution of High-Order BAM Neural Networks with Continuously Distributed Delays and Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Chang-Bo Yang ◽  
Ting-Zhu Huang ◽  
Jin-Liang Shao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Functional Method ◽  
High Order ◽  
Distributed Delays ◽  
Bam Neural Networks ◽  
New Type ◽  
Lyapunov Functional Method

ByM-matrix theory, inequality techniques, and Lyapunov functional method, certain sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of periodic solution for a new type of high-order BAM neural networks with continuously distributed delays and impulses. These novel conditions extend and improve some previously known results in the literature. Finally, an illustrative example and its numerical simulation are given to show the feasibility and correctness of the derived criteria.

scholarly journals Asymptotic Stability and Exponential Stability of Impulsive Delayed Hopfield Neural Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jing Chen ◽  
Xiaodi Li ◽  
Dequan Wang
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Uniform Asymptotic Stability ◽  
Linear Matrix Inequality Approach

A criterion for the uniform asymptotic stability of the equilibrium point of impulsive delayed Hopfield neural networks is presented by using Lyapunov functions and linear matrix inequality approach. The criterion is a less restrictive version of a recent result. By means of constructing the extended impulsive Halanay inequality, we also analyze the exponential stability of impulsive delayed Hopfield neural networks. Some new sufficient conditions ensuring exponential stability of the equilibrium point of impulsive delayed Hopfield neural networks are obtained. An example showing the effectiveness of the present criterion is given.

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