G−布朗运动驱动的时滞神经网络的稳定性分析

Stability analysis for time-delayed neural networks driven by G−Brownian motion

研究一类由G−布朗运动驱动的时滞神经网络(G−DNN)的稳定性问题.实际中噪声并不总是服从正态分布,为更好地描述实际情形,采用G−布朗运动来描述噪声,分析G−布朗运动噪声的离散观测值对时滞神经网络稳定性的影响.针对指数稳定的时滞神经网络,引入由G−布朗运动驱动的随机噪声,并利用G−随机分析理论、Gronwall不等式、Borel-Cantelli引理等,给出随机噪声强度的上界,使得在噪声强度少于该上界的情形下随机时滞递归神经网络的稳定速度大于原来神经网络的稳定速度.进一步分析噪声在离散的情形下随机时滞递归神经网络的稳定性问题.借助G−Itô公式、放缩技巧及一些基本不等式,得到能进一步加快随机时滞递归神经网络指数稳定速度的噪声离散步长的上界.通过实例验证了理论结果的有效性.

The stability problem was investigated for a class of time-delayed neural networks driven by G−Brownian motion(G−DNNs).The random noise does not always obeys a normal distribution,in order to better describe the actual situation,G−Brownian motion was used to describe the noise,and the influence of discrete-time observations of G-Brownian motion noise on the stability of time-delayed neural networks was analyzed.For exponentially stable time-delayed neural networks,the random noise driven by G-Brownian motion was introduced,the upper bound of random noise intensity was given by using G−random analysis theory,Gronwall inequality,and Borel-Cantelli lemma,and when the noise intensity was less than the upper bound,the stability speed of stochastic delayed recurrent neural networks was faster than that of the original.The stability of stochastic delayed recurrent neural networks was further analyzed in the case of discrete-time noise.By using the G−Itôformula,scaling technique,and some basic inequalities,the upper bound was obtained for the discrete-time step size of the noise and the stability of the stochastic delayed recurrent neural networks was further accelerated.The validity of theoretical results was verified by an example.