Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks  

作　　者：Yu-Jiao Huang Xiao-Yan Yuan Xu-Hua Yang Hai-Xia Long Jie Xiao 黄玉娇;袁孝焰;杨旭华;龙海霞;肖杰(Zhijiang College,Zhejiang University of Technology,Hangzhou 310024,China;College of Computer Science and Technology,Zhejiang University of Technology,Hangzhou 310023,China)

机构地区：[1]Zhijiang College,Zhejiang University of Technology,Hangzhou 310024,China [2]College of Computer Science and Technology,Zhejiang University of Technology,Hangzhou 310023,China

出　　处：《Chinese Physics B》2020年第2期196-205,共10页中国物理B（英文版）

基　　金：Project supported by the Natural Science Foundation of Zhejiang Province of China(Grant Nos.LY18F030023,LY17F030016,LQ18F030015,and LY18F020028);the National Natural Science Foundation of China(Grant Nos.61503338,61773348,and 61972354).

摘　　要：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=1^n(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=1^n(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.This paper addresses the coexistence and local stability of multiple equilibrium points for fractional-order CohenGrossberg neural networks（FOCGNNs） with time delays.Based on Brouwer’s fixed point theorem,sufficient conditions are established to ensure the existence of Πi=1n（2 Ki+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.

关 键 词：FRACTIONAL-ORDER COHEN-GROSSBERG neural networks MULTIPLE LAGRANGE STABILITY MULTIPLE LYAPUNOV asymptotical STABILITY time delays 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] TP183[自动化与计算机技术—控制科学与工程]