Global Well-Posedness and Dynamical Behavior of Delayed Reaction-Diffusion BAM Neural Networks Driven by Wiener Processes

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.

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

Abstract and Applied Analysis ◽

10.1155/2013/645262 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 3

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.

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Adaptive stochastic synchronization of delayed reaction–diffusion neural networks

Measurement and Control ◽

10.1177/0020294019893056 ◽

2020 ◽

Vol 53 (3-4) ◽

pp. 378-389 ◽

Cited By ~ 1

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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