title: Multistability of Delayed Recurrent Neural Networks with Mexican Hat Activation Functions.
abstract: 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.
authors.affiliation: 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. liupengjz@163.com.
authors.forename: Peng
authors.initials: P
authors.lastname: Liu
authors.affiliation: 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. zgzeng@hust.edu.cn.
authors.forename: Zhigang
authors.initials: Z
authors.lastname: Zeng
authors.affiliation: Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong jwang.cs@cityu.edu.hk.
authors.forename: Jun
authors.initials: J
authors.lastname: Wang
mesh_terms: D003198:Computer Simulation; D016571:Neural Networks, Computer