Multistability of complex-valued recurrent neural networks with real-imaginary-type activation functions
Multistability of complex-valued recurrent neural networks with real-imaginary-type activation functions
复制标题
具有实虚型激活函数的复值循环神经网络的多稳定性
DOI：
10.1016/j.amc.2013.12.027
复制
发表时间：
2014-02-25
影响因子：
4
通讯作者：
Wang, Zhanshan
中科院分区：
文献类型：
--
作者：
Huang, Yujiao;Zhang, Huaguang;Wang, Zhanshan
本文研究具有实虚型激活函数的n维复值递归神经网络的多重稳定性问题。给出了[(2α+1)(2β+1)](N)(α，β>；=1)平衡点存在的充分条件。在这些条件下，((α+1)(β+1)](N)平衡点是局部指数稳定的，而其他平衡点是不稳定的。此外，还研究了具有吸引力的平衡态盆地。得到了一维复值递归神经网络平衡点的完全吸引盆。所得稳定性结果改进和推广了已有的稳定性结果。给出了两个数值算例，说明了所得结果的有效性。(C)2013 Elsevier Inc.保留所有权利。
This paper addresses the multistability problem of n-dimensional complex-valued recurrent neural networks with real-imaginary-type activation functions. Sufficient conditions are proposed for checking the existence of [(2 alpha + 1)(2 beta+ 1)](n) (alpha, beta >= 1) equilibria. Under these conditions, ((alpha + 1)(beta + 1)](n) equilibria are locally exponentially stable and the others are unstable. Attractive basins of equilibria are also investigated. Complete attractive basins of equilibria in 1-dimensional complex-valued recurrent neural networks are obtained. The obtained stability results improve and extend the existing ones. Two numerical examples are given to illustrate the effectiveness of the obtained results. (C) 2013 Elsevier Inc. All rights reserved.