scholarly journals Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Li Wan ◽  
Qinghua Zhou ◽  
Jizi Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Ultimate Boundedness ◽  
Dynamical Behaviors ◽  
Weak Attractor ◽  
Stochastic Reaction ◽  
Theoretical Results

This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical 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.

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.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

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.

Delayed Reaction–Diffusion Cellular Neural Networks of Fractional Order: Mittag–Leffler Stability and Synchronization

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Ivanka M. Stamova ◽  
Stanislav Simeonov
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Delayed Reaction

This research introduces a model of a delayed reaction–diffusion fractional neural network with time-varying delays. The Mittag–Leffler-type stability of the solutions is investigated, and new sufficient conditions are established by the use of the fractional Lyapunov method. Mittag–Leffler-type synchronization criteria are also derived. Three illustrative examples are established to exhibit the proposed sufficient conditions.

scholarly journals Dynamical Behaviors of Impulsive Stochastic Reaction-Diffusion Neural Networks with Mixed Time Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Weiyuan Zhang ◽  
Junmin Li ◽  
Minglai Chen
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Mixed Time Delays ◽  
Dynamical Behaviors ◽  
Proposed Model ◽  
The Mean ◽  
Stochastic Reaction

We discuss the dynamical behaviors of impulsive stochastic reaction-diffusion neural networks (ISRDNNs) with mixed time delays. By using a well-knownL-operator differential inequality with mixed time delays and combining with the Lyapunov-Krasovkii functional approach, as well as linear matrix inequality (LMI) technique, some novel sufficient conditions are derived to ensure the existence, uniqueness, and global exponential stability of the periodic solutions for ISRDNNs with mixed time delays in the mean square sense. The obtained sufficient conditions depend on the reaction-diffusion terms. The results of this paper are new and improve some of the previously known results. The proposed model is quite general since many factors such as noise perturbations, impulsive phenomena, and mixed time delays are considered. Finally, two numerical examples are provided to verify the usefulness of the obtained results.

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