摘要
研究了Ｈｏｐｆｉｅｌｄ型随机时滞神经网络ｄｘ（ｔ）＝［－Ａｘ（ｔ）＋Ｂσ（ｘ（ｔ一τ））］ｄｔ＋ｆ（ｔ．ｘ（ｔ），Ｘ（ｔ—τ））ｄｗ（ｔ）的均方指数稳定性与几乎必然指数稳定性．应用Ｌａｙａｐｕｎｏｖ函数与鞅不等式，建立了这种随机时滞神经网络指数稳定的时滞相关的充分条件．文献中某些关于确定性的时滞神经网络ｘ（ｔ）＝－Ａｘ（ｔ）＋Ｂσ（ｘ（ｔ－τ））与神经网络ｘ（ｔ）＝－Ａｘ（ｔ）＋Ｂσ（ｘ（ｔ））的稳定准则是文中的特殊情况．
In this paper the exponential stability in mean square and almost surely expo- nential stability. are investigated for stochastic neural networks with delay of the form dx(t) = [-Ax(t) + Bσ(x(t - τ) )]dt + f(t,x(t),x(t - τ) )dw(t). For such neural networks, several sufficient conditions for the exponential stability are established by the Lyapunov function method together with martigale inequalities, The obtained results are dependent of the size of delay. Some stability criteria in the literature for the deterministic neural networks with delay x(t) = - Ax(t) + Bσ(x(t - τ) ) and neural networks x(t) - Ax(t) + Bσ(x(t) ) are included as special cases.
出处
《数学物理学报（A辑）》
CSCD
北大核心
1999年第2期211-218,共8页
Acta Mathematica Scientia
基金
国家教委博士点基金
国家自然科学基金
关键词
随机时滞神经网络
HOPFIELD型
指数稳定
Stochastic delay neural network, Lyapunov function, Martigale inequality, Exponential stability.
