scholarly journals Stability of the Stochastic Reaction-Diffusion Neural Network with Time-Varying Delays andp-Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Pan Qingfei ◽  
Zhang Zifang ◽  
Huang Jingchang
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Reaction Diffusion ◽  
Time Varying ◽  
The Neural Network ◽  
The Moment ◽  
Delay Differential ◽  
Stochastic Reaction ◽  
Moment Exponential Stability ◽  
Delay Differential Inequality

The main aim of this paper is to discuss moment exponential stability for a stochastic reaction-diffusion neural network with time-varying delays andp-Laplacian. Using the Itô formula, a delay differential inequality and the characteristics of the neural network, the algebraic conditions for the moment exponential stability of the nonconstant equilibrium solution are derived. An example is also given for illustration.

scholarly journals Stability Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Time-Varying Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Chuangxia Huang ◽  
Xinsong Yang ◽  
Yigang He
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Stochastic Analysis ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Inequality Techniques ◽  
Stochastic Reaction ◽  
Moment Exponential Stability

This paper is concerned withpth moment exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. With the help of Lyapunov method, stochastic analysis, and inequality techniques, a set of new suffcient conditions onpth moment exponential stability for the considered system is presented. The proposed results generalized and improved some earlier publications.

MEAN VALUE EXPONENTIAL STABILITY OF STOCHASTIC REACTION–DIFFUSION GENERALIZED COHEN–GROSSBERG NEURAL NETWORKS WITH TIME-VARYING DELAY

2007 ◽  
Vol 17 (09) ◽  
pp. 3219-3227 ◽  
Author(s):  
LI WAN ◽  
QINGHUA ZHOU ◽  
JIANHUA SUN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Mean Value ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Stability ◽  
Stochastic Reaction ◽  
Varying Delay

Stochastic effects on the stability property of reaction–diffusion generalized Cohen–Grossberg neural networks (GDCGNNs) with time-varying delay are considered. By skillfully constructing suitable Lyapunov functionals and employing the method of variational parameters, inequality technique and stochastic analysis, the delay independent and easily verifiable sufficient conditions to guarantee the mean-value exponential stability of an equilibrium solution associated with temporally uniform external inputs to the networks are obtained. One example is given to illustrate the theoretical results.

EXPONENTIAL p-STABILITY OF STOCHASTIC REACTION–DIFFUSION CELLULAR NEURAL NETWORKS WITH MULTIPLE DELAYS

2009 ◽  
Vol 19 (10) ◽  
pp. 3373-3386 ◽  
Author(s):  
RANCHAO WU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Matrix Analysis ◽  
Multiple Delays ◽  
Space Matrix ◽  
Stochastic Reaction ◽  
Moment Exponential Stability

In the current paper, a class of stochastic cellular neural networks with reaction–diffusion effects, both discrete and distributed time delays, is studied. Several sufficient conditions guaranteeing the almost sure and pth moment exponential stability of its equilibrium solution are respectively obtained through analytic methods such as employing Lyapunov functional, applying Itô's formula, inequality techniques, embedding in Banach space, Matrix analysis and semimartingale convergence theorem. The yielded conclusions, which are independent of diffusion terms and delays, assume much less restrictions on activation functions and interconnection weights, and can be applied within a broader range of neural networks. Moreover, through the obtained results, it could be noted that noise will affect the exponential stability of the system. For illustration, two examples are given to show the feasibility of results.

scholarly journals Exponential Stability and Periodicity of Fuzzy Delayed Reaction-Diffusion Cellular Neural Networks with Impulsive Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guowei Yang ◽  
Yonggui Kao ◽  
Changhong Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Impulsive Effect ◽  
Time Varying ◽  
Delayed Reaction

This paper considers dynamical behaviors of a class of fuzzy impulsive reaction-diffusion delayed cellular neural networks (FIRDDCNNs) with time-varying periodic self-inhibitions, interconnection weights, and inputs. By using delay differential inequality,M-matrix theory, and analytic methods, some new sufficient conditions ensuring global exponential stability of the periodic FIRDDCNN model with Neumann boundary conditions are established, and the exponential convergence rate index is estimated. The differentiability of the time-varying delays is not needed. An example is presented to demonstrate the efficiency and effectiveness of the obtained results.

Artificial neural networks in the problem of determining the position and size of the solar disk in wide-angle photographs of the sky

2021 ◽  
Author(s):  
Mikhail Borisov ◽  
Mikhail Krinitskiy
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Solar Disk ◽  
Weather Conditions ◽  
Wide Angle ◽  
Know How ◽  
The Neural Network ◽  
Artificial Neural ◽  
The Moment

<p>Total cloud score is a characteristic of weather conditions. At the moment, there are algorithms that automatically calculate cloudiness based on a photograph of the sky These algorithms do not know how to find the solar disk, so their work is not absolutely accurate.</p><p>To create an algorithm that solves this data, the data used, obtained as a result of sea research voyages, is used, which is marked up for training the neural network.</p><p>As a result of the work, an algorithm was obtained based on neural networks, based on a photograph of the sky, in order to determine the size and position of the solar disk, other algorithms can be used to work with images of the visible hemisphere of the sky.</p>

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