随机细胞人工神经网络的稳定性

基于细胞神经网络输出函数饱和线性特性,采用分割状态空间为若干子区域的方法,对处于噪声环境下的细胞神经网络的几乎必然指数稳定性进行了分析.在噪声扰动项分别满足Lipschitz条件和线性条件下,依据平衡点所处子区域位置,得到了对应区域中仅依赖于网络参数构成的矩阵负定性的若干代数判别条件.特别地,如果平衡点为区域内点,所得结果是非常方便检验的.研究结果可供网络设计参考,并可用来计算网络抗干扰强度.

Stability of stochastic cellular neural networks

The output functions of neurons in cellular neural networks are characterized by saturation linearity. A method to divide the state space into sub-domains adopted to study almost sure exponential stability over the cellular neural networks under noise environment. When Lipschitz condition and linear growth condition on perturbed terms of the model of the network are satisfied, some algebraic criteria are obtained which are only related to the parameters of the network itself. The results show that some appropriate negative definite matrices, which are related to the position of the equilibrium of the network, ensure the network to be almost sure exponentially stable. In particular, if the equilibrium of the network is in the interior of a sub-domain, the obtained conclusions are conveniently tested. All the results can be used to compute the perturbed intensity of networks.