scholarly journals Exponential Stability for a Class of Stochastic Reaction-Diffusion Hopfield Neural Networks with Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Xiao Liang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Hopfield Neural Networks ◽  
Chebyshev Inequality ◽  
Delayed Reaction ◽  
Wiener Processes ◽  
Analysis Technique ◽  
Mean Square Exponential Stability

This paper studies the asymptotic behavior for a class of delayed reaction-diffusion Hopfield neural networks driven by finite-dimensional Wiener processes. Some new sufficient conditions are established to guarantee the mean square exponential stability of this system by using Poincaré’s inequality and stochastic analysis technique. The proof of the almost surely exponential stability for this system is carried out by using the Burkholder-Davis-Gundy inequality, the Chebyshev inequality and the Borel-Cantelli lemma. Finally, an example is given to illustrate the effectiveness of the proposed approach, and the simulation is also given by using the Matlab.

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.

scholarly journals Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Chuangxia Huang ◽  
Xinsong Yang ◽  
Yigang He ◽  
Lehua Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Distributed Delays ◽  
Almost Sure Exponential Stability ◽  
Mean Square Exponential Stability ◽  
Stochastic Reaction

Stability of reaction-diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov's functional method, M-matrix properties, some inequality technique, and nonnegative semimartingale convergence theorem are used in our approach. The obtained conclusions improve some published results.

scholarly journals Exponential Stability of Impulsive Delayed Reaction-Diffusion Cellular Neural Networks via Poincaré Integral Inequality

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xianghong Lai ◽  
Tianxiang Yao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Integral Inequality ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Stability Study ◽  
Delayed Reaction ◽  
Regional Features ◽  
The Stability

This work is devoted to the stability study of impulsive cellular neural networks with time-varying delays and reaction-diffusion terms. By means of new Poincaré integral inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some novel and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The provided stability criteria are applicable to Dirichlet boundary condition and show that not only the reaction-diffusion coefficients but also the regional features including the boundary and dimension of spatial variable can influence the stability. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results.

scholarly journals Mean Square Exponential Stability of Stochastic Cohen-Grossberg Neural Networks with Unbounded Distributed Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Chuangxia Huang ◽  
Lehua Huang ◽  
Yigang He
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Mean Square ◽  
State Variables ◽  
Analysis Technique ◽  
Mean Square Exponential Stability ◽  
Unbounded Distributed Delays ◽  
Inequality Techniques

This paper addresses the issue of mean square exponential stability of stochastic Cohen-Grossberg neural networks (SCGNN), whose state variables are described by stochastic nonlinear integrodifferential equations. With the help of Lyapunov function, stochastic analysis technique, and inequality techniques, some novel sufficient conditions on mean square exponential stability for SCGNN are given. Furthermore, we also establish some sufficient conditions for checking exponential stability for Cohen-Grossberg neural networks with unbounded distributed delays.

CONVERGENCE DYNAMICS OF STOCHASTIC REACTION–DIFFUSION RECURRENT NEURAL NETWORKS WITH DELAYS

2005 ◽  
Vol 15 (07) ◽  
pp. 2131-2144 ◽  
Author(s):  
JIANHUA SUN ◽  
LI WAN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Reaction Diffusion ◽  
Mean Value ◽  
Almost Sure Exponential Stability ◽  
Transmission Delays ◽  
Mean Square Exponential Stability

Stochastic effects on convergence dynamics of reaction–diffusion recurrent neural networks (RNNs) with constant transmission delays are studied. Without assuming the boundedness, monotonicity and differentiability of the activation functions, nor symmetry of synaptic interconnection weights, by skillfully constructing suitable Lyapunov functionals and employing the method of variational parameters, M-matrix properties, inequality technique, stochastic analysis and non-negative semimartingale convergence theorem, delay independent and easily verifiable sufficient conditions to guarantee the almost sure exponential stability, mean value exponential stability and mean square exponential stability of an equilibrium solution associated with temporally uniform external inputs to the networks are obtained, respectively. The results are compared with the previous results derived in the literature for discrete delayed RNNs without diffusion or stochastic perturbation. Two examples are also given to demonstrate our results.

scholarly journals Adaptive stochastic synchronization of delayed reaction–diffusion neural networks

2020 ◽  
Vol 53 (3-4) ◽  
pp. 378-389 ◽  
Author(s):  
Weiyuan Zhang ◽  
Junmin Li ◽  
Jinghan Sun ◽  
Minglai Chen
Keyword(s):  
Neural Networks ◽  
Feedback Control ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Output Coupling ◽  
Delayed Reaction ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Stochastic Synchronization

In this paper, we deal with the adaptive stochastic synchronization for a class of delayed reaction–diffusion neural networks. By combing Lyapunov–Krasovskii functional, drive-response concept, the adaptive feedback control scheme, and linear matrix inequality method, we derive some sufficient conditions in terms of linear matrix inequalities ensuring the stochastic synchronization of the addressed neural networks. The output coupling with delay feedback and the update laws of parameters for adaptive feedback control are proposed, which will be of significance in the real application. The novel Lyapunov–Krasovskii functional to be constructed is more general. The derived results depend on the measure of the space, diffusion effects, and the upper bound of derivative of time-delay. Finally, an illustrated example is presented to show the effectiveness and feasibility of the proposed scheme.

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