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Zbl 1122.34065
Wang, Zidong; Shu, Huisheng; Fang, Jian'an; Liu, Xiaohui
Robust stability for stochastic Hopfield neural networks with time delays. (English)
[J] Nonlinear Anal., Real World Appl. 7, No. 5, 1119-1128 (2006). ISSN 1468-1218

The Hopfield neural network is described by a stochastic delay differential equation of the form $$dx(t)=(-Ax(t)+W l(x(t-h)))dt+(Cx(t)+Dx(t-h))dw(t).$$ Here $A,W,C,D$ are matrices with certain properties, $l$ is a Lipschitz continuous neuron activity function and $w$ is a Brownian motion. It is shown that certain explicit matrix inequalities imply that the equilibrium solution is robustly, globally, asymptotically stable in the mean-square sense.
[Markus Reiss (Heidelberg)]

MSC 2000:: *34K50 Stochastic delay equations
34K20 Stability theory of functional-differential equations
93D09 Robust stability of control systems
92B20 General theory of neural networks

Keywords: Hopfield neural network; stochastic delay system; Lyapunov-Krasovskii functional

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