title: Multistability analysis of a general class of recurrent neural networks with non-monotonic activation functions and time-varying delays.
abstract: This paper addresses the multistability for a general class of recurrent neural networks with time-varying delays. Without assuming the linearity or monotonicity of the activation functions, several new sufficient conditions are obtained to ensure the existence of (2K+1)(n) equilibrium points and the exponential stability of (K+1)(n) equilibrium points among them for n-neuron neural networks, where K is a positive integer and determined by the type of activation functions and the parameters of neural network jointly. The obtained results generalize and improve the earlier publications. Furthermore, the attraction basins of these exponentially stable equilibrium points are estimated. It is revealed that the attraction basins of these exponentially stable equilibrium points can be larger than their originally partitioned subsets. Finally, three illustrative numerical examples show the effectiveness of theoretical results.
authors.affiliation: School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China. Electronic address: liupengjz@163.com.
authors.forename: Peng
authors.initials: P
authors.lastname: Liu
authors.affiliation: School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China. Electronic address: hustzgzeng@gmail.com.
authors.forename: Zhigang
authors.initials: Z
authors.lastname: Zeng
authors.affiliation: Department of Computer Science, College of Science and Engineering, City University of Hong Kong, Kowloon Tong, Hong Kong. Electronic address: jwang.cs@cityu.edu.hk.
authors.forename: Jun
authors.initials: J
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016571:Neural Networks, Computer; D009474:Neurons; D013997:Time Factors
keywords: Cohen–Grossberg neural networks; Multistability; Non-monotonic activation functions; Time-varying delays