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Chin. Phys. B, 2020, Vol. 29(2): 020703    DOI: 10.1088/1674-1056/ab6716
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Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks

Yu-Jiao Huang(黄玉娇)1,2, Xiao-Yan Yuan(袁孝焰)2, Xu-Hua Yang(杨旭华)2, Hai-Xia Long(龙海霞)2, Jie Xiao(肖杰)2
1 Zhijiang College, Zhejiang University of Technology, Hangzhou 310024, China;
2 College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China
Abstract  This paper addresses the coexistence and local stability of multiple equilibrium points for fractional-order Cohen-Grossberg neural networks (FOCGNNs) with time delays. Based on Brouwer's fixed point theorem, sufficient conditions are established to ensure the existence of Πi=1n(2Ki+1) equilibrium points for FOCGNNs. Through the use of Hardy inequality, fractional Halanay inequality, and Lyapunov theory, some criteria are established to ensure the local Lagrange stability and the local Lyapunov asymptotical stability of Πi=1n(Ki+1) equilibrium points for FOCGNNs. The obtained results encompass those of integer-order Hopfield neural networks with or without delay as special cases. The activation functions are nonlinear and nonmonotonic. There could be many corner points in this general class of activation functions. The structure of activation functions makes FOCGNNs could have a lot of stable equilibrium points. Coexistence of multiple stable equilibrium points is necessary when neural networks come to pattern recognition and associative memories. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained results.
Keywords:  fractional-order Cohen-Grossberg neural networks      multiple Lagrange stability      multiple Lyapunov asymptotical stability      time delays  
Received:  24 June 2019      Revised:  06 November 2019      Accepted manuscript online: 
PACS:  07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)  
  02.30.Ks (Delay and functional equations)  
Fund: Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. LY18F030023, LY17F030016, LQ18F030015, and LY18F020028) and the National Natural Science Foundation of China (Grant Nos. 61503338, 61773348, and 61972354).
Corresponding Authors:  Xu-Hua Yang     E-mail:  xhyang@zjut.edu.cn

Cite this article: 

Yu-Jiao Huang(黄玉娇), Xiao-Yan Yuan(袁孝焰), Xu-Hua Yang(杨旭华), Hai-Xia Long(龙海霞), Jie Xiao(肖杰) Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks 2020 Chin. Phys. B 29 020703

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