# 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 booklet experiences at the most recent findings within the learn of Stochastic Neural Networks (SNN). The booklet collects the radical version of the disturbance pushed by way of Levy technique, the examine approach to M-matrix, and the adaptive regulate approach to the SNN within the context of balance and synchronization keep watch over. The ebook may be of curiosity to school researchers, graduate scholars up to the mark technology and engineering and neural networks who desire to study the center ideas, equipment, algorithms and functions of SNN.

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**Example text**

7) achieve synchronization. Next, we denote ei (t) = xi (t) −r (t), which indicates the error signal. 6), the error signal system can be easily obtained as follows: ⎡ t dei (t) = ⎣−Cei (t) + Ag(ei (t)) + Bg(ei (t − τ )) + W ⎤ g(ei (s))ds ⎦ dt t−τ N + ci N G i j Γ e j (t)d Wi1 (t) + di j=1 G i j Γτ e j (t − τ )d Wi2 (t) + Ui dt, i = 1, 2, . . 11) where g(ei (t)) = f (ei (t) + r (t)) − f (r (t)) and g(ei (t − τ )) = f (ei (t − τ ) + r (t − τ )) − f (r (t − τ )). 12) where M = diag{β1 , β2 , β3 , .

Appl. 38(1), 121– 130 (2011) 4. R. Belohlavek, Fuzzy logical bidirectional associative memory. Inf. Sci. 128(1), 91–103 (2000) 5. J. Cao, P. Li, W. Wang, Global synchronization in arrays of delayed neural networks with constant and delayed coupling. Phys. 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.

5) j=1 where xi (t) = [xi1 (t), xi2 (t), . . , 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 .