Liu Peng, Zeng Zhigang, Wang Jun
School of Automation, Huazhong University of Science and Technology, China, and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, P.R.C.
Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong
Neural Comput. 2017 Feb;29(2):423-457. doi: 10.1162/NECO_a_00922. Epub 2016 Dec 28.
This letter studies the multistability analysis of delayed recurrent neural networks with Mexican hat activation function. Some sufficient conditions are obtained to ensure that an [Formula: see text]-dimensional recurrent neural network can have [Formula: see text] equilibrium points with [Formula: see text], and [Formula: see text] of them are locally exponentially stable. Furthermore, the attraction basins of these stable equilibrium points are estimated. We show that the attraction basins of these stable equilibrium points can be larger than their originally partitioned subsets. The results of this letter improve and extend the existing stability results in the literature. Finally, a numerical example containing different cases is given to illustrate the theoretical results.
本文研究了具有墨西哥帽激活函数的时滞递归神经网络的多重稳定性分析。获得了一些充分条件，以确保一个[公式：见原文]维递归神经网络可以具有[公式：见原文]个平衡点，其中[公式：见原文]个是局部指数稳定的。此外，还估计了这些稳定平衡点的吸引域。我们表明，这些稳定平衡点的吸引域可以大于它们原来划分的子集。本文的结果改进并扩展了文献中现有的稳定性结果。最后，给出了一个包含不同情况的数值例子来说明理论结果。
