scholarly journals Dynamical Behaviors of Stochastic Hopfield Neural Networks with Both Time-Varying and Continuously Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Qinghua Zhou ◽  
Penglin Zhang ◽  
Li Wan
Keyword(s):  
Neural Networks ◽  
Hopfield Neural Networks ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Ultimate Boundedness ◽  
Functional Theory ◽  
Dynamical Behaviors ◽  
Theoretical Results

This paper investigates dynamical behaviors of stochastic Hopfield neural networks with both time-varying and continuously distributed delays. By employing the Lyapunov functional theory and linear matrix inequality, some novel criteria on asymptotic stability, ultimate boundedness, and weak attractor are derived. Finally, an example is given to illustrate the correctness and effectiveness of our theoretical results.

Dynamical Behaviors of Stochastic Reaction-Diffusion Hopfield Neural Networks

2013 ◽  
Vol 787 ◽  
pp. 921-925
Author(s):  
Qing Hua Zhou ◽  
Li Wan
Keyword(s):  
Neural Networks ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Ultimate Boundedness ◽  
Dynamical Behaviors ◽  
Diffusion Effects ◽  
Stochastic Reaction ◽  
Theoretical Results

Dynamical behaviors of stochastic reaction-diffusion Hopfield neural networks with delays are investigated. By employing Lyapunov method, Hardy-Poincare inequality and linear matrix inequality, some novel criteria on ultimate boundedness and asymptotic stability are obtained. The sufficient criteria depend on the diffusion effects and are independent of the magnitude of the delays. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical 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.

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.

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 Synchronization of Switched Complex Bipartite Neural Networks with Infinite Distributed Delays and Derivative Coupling

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
Qiuxiang Bian ◽  
Jinde Cao ◽  
Jie Wu ◽  
Hongxing Yao ◽  
Tingfang Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lmi Approach ◽  
Derivative Coupling ◽  
Infinite Distributed Delays ◽  
Theoretical Results

A new model of switched complex bipartite neural network (SCBNN) with infinite distributed delays and derivative coupling is established. Using linear matrix inequality (LMI) approach, some synchronization criteria are proposed to ensure the synchronization between two SCBNNs by constructing effective controllers. Some numerical simulations are provided to illustrate the effectiveness of the theoretical results obtained in this paper.

Dynamical Behaviors of Stochastic Hopfield Neural Networks with Reaction-Diffusion Terms

2013 ◽  
Vol 432 ◽  
pp. 523-527
Author(s):  
Qing Hua Zhou ◽  
Li Wan
Keyword(s):  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Hopfield Neural Network ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ultimate Boundedness ◽  
Dynamical Behaviors ◽  
Diffusion Effects ◽  
Weak Attractor ◽  
Theoretical Results

Dynamical behaviors of stochastic Hopfield neural network with delays and reaction-diffusion terms are investigated. By employing Lyapunov method, Poincare inequality and linear matrix inequality, some novel criteria on ultimate boundedness, weak attractor and asymptotic stability are obtained. The criteria are independent of the magnitude of the delays, and dependent on the diffusion effects and the derivative of the delays. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

scholarly journals Dynamical Behaviors of the Stochastic Hopfield Neural Networks with Mixed Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li Wan ◽  
Qinghua Zhou ◽  
Zhigang Zhou ◽  
Pei Wang
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Functional Differential Equations ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Mixed Time Delays ◽  
Dynamical Behaviors ◽  
Functional Differential ◽  
Theoretical Results ◽  
Stochastic Functional

This paper investigates dynamical behaviors of the stochastic Hopfield neural networks with mixed time delays. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. By employing the theory of stochastic functional differential equations and linear matrix inequality (LMI) approach, some novel criteria on asymptotic stability, ultimate boundedness, and weak attractor are derived. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

Stability Criterion of Discrete Hopfield Neural Networks with Multiple Delays in Parallel Mode: Linear Matrix Inequality

2011 ◽  
Vol 225-226 ◽  
pp. 1270-1273
Author(s):  
Xiao Feng Lai ◽  
Xing Yin ◽  
Hai Yang Zou
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Stability Criterion ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Matrix Inequality ◽  
Parallel Mode

In this paper, Discrete Hopfield Neural Networks with Multple Delays is introduced.And a stability criterion of Discrete Hopfield Neural Networks with Multple Delays is studied bythe linear matrix inequality. It provides a theory basis for the application of Discrete Hopfield Neural Networks with Multple Delays.

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