Stability and Synchronization Control of Stochastic Neural by Wuneng Zhou, Jun Yang, Liuwei Zhou, Dongbing Tong

By Wuneng Zhou, Jun Yang, Liuwei Zhou, Dongbing Tong

This book reports at the most recent findings within the learn of Stochastic Neural Networks (SNN). The publication collects the unconventional version of the disturbance pushed by means of Levy procedure, the examine approach to M-matrix, and the adaptive keep an eye on approach to the SNN within the context of balance and synchronization regulate. The publication could be of curiosity to college researchers, graduate scholars up to the mark technological know-how and engineering and neural networks who desire to study the middle rules, tools, algorithms and purposes of SNN.

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Extra info for Stability and Synchronization Control of Stochastic Neural Networks

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26]. And, in Ref. [30], on the basis of Lyapunov stability theory, time-delay feedback control and other techniques, the exponential synchronization problem of a class of stochastic perturbed chaotic delayed neural networks was considered. It is well known that, time-delays are often encountered in many kinds of neural networks, which can be the sources of oscillation and instability of neural networks [25, 28, 29, 31–33]. However, from the literature mentioned above, we can find that only discrete time-delay has been considered.

Lett. A 353(4), 318–325 (2006) 6. J. Cao, X. Li, Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach. Phys. D 212(1), 54–65 (2005) 7. J. Cao, Z. Wang, Y. Sun, Synchronization in an array of linearly stochastically coupled networks with time-delays. Phys. A: Stat. Mech. Appl. 385(2), 718–728 (2007) 8. R. Chen, J. R. Liu, Global synchronization of coupled delayed neural networks and applications to chaotic CNN model. Int. J. Bifurc. Chaos 14(7), 2229–2240 (2004) 9. M. Chen, D.

Xin (t)]T ∈ Rn (i = 1, 2, . . , N ) is the state vector associated with the ith DNNs; f (xi (t)) = [ f 1 (xi1 (t)), f 2 (xi2 (t)), . . , f n (xin (t))]T ∈ Rn is the activation functions of the neurons with f (0) = 0; C = diag{c1 , c2 , . . , cn } > 0 is a diagonal matrix that shows the rate of the ith unit resetting its potential to the resting state in isolation when disconnected from the external inputs and the network; A = (ai j )n×n and B = (bi j )n×n stand for, respectively, the connection weight matrix and the discretely delayed connection weight matrix; Wi = [Wi1 , Wi2 ]T are two-dimensional Brownian motions; Γ ∈ Rn×n and Γτ ∈ Rn×n denotes the internal coupling of the network at time t and t − τ , where τ > 0 is the time-delay; ci and di indicate the intensity of the noise; Ui is the input of the controller; G = (G i j ) N ×N describes the topological structure and the coupling strength of the networks, and it meet the following conditions [27]: N G ii = − Gi j .

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