Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays

He Huang; Daniel W.C. Ho; Jinde Cao

doi:10.1016/j.neunet.2004.11.002

Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays

He Huang, Daniel W.C. Ho, Jinde Cao

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

55 Citations (Scopus)

Abstract

In this paper, a general class of recurrent neural networks with time-varying delays is studied. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point and the existence of periodic solutions for such delayed neural networks. Comparing with some previous literature, in which the time-varying delays were assumed to be differentiable and their derivatives were simultaneously required to be not greater than 1, the restrictions on the time-varying delays are removed. Therefore, our results obtained here improve and extend some previously related results. Finally, two numerical examples are provided to illustrate our theorems. © 2004 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	161-170
Journal	Neural Networks
Volume	18
Issue number	2
DOIs	https://doi.org/10.1016/j.neunet.2004.11.002
Publication status	Published - Mar 2005

Research Keywords

Global exponential stability
Neural networks
Nonsingular M-matrix
Periodic solutions
Time-varying delays

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title = "Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays",

abstract = "In this paper, a general class of recurrent neural networks with time-varying delays is studied. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point and the existence of periodic solutions for such delayed neural networks. Comparing with some previous literature, in which the time-varying delays were assumed to be differentiable and their derivatives were simultaneously required to be not greater than 1, the restrictions on the time-varying delays are removed. Therefore, our results obtained here improve and extend some previously related results. Finally, two numerical examples are provided to illustrate our theorems. {\textcopyright} 2004 Elsevier Ltd. All rights reserved.",

keywords = "Global exponential stability, Neural networks, Nonsingular M-matrix, Periodic solutions, Time-varying delays",

author = "He Huang and Ho, {Daniel W.C.} and Jinde Cao",

year = "2005",

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TY - JOUR

T1 - Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays

AU - Huang, He

AU - Ho, Daniel W.C.

AU - Cao, Jinde

PY - 2005/3

Y1 - 2005/3

N2 - In this paper, a general class of recurrent neural networks with time-varying delays is studied. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point and the existence of periodic solutions for such delayed neural networks. Comparing with some previous literature, in which the time-varying delays were assumed to be differentiable and their derivatives were simultaneously required to be not greater than 1, the restrictions on the time-varying delays are removed. Therefore, our results obtained here improve and extend some previously related results. Finally, two numerical examples are provided to illustrate our theorems. © 2004 Elsevier Ltd. All rights reserved.

AB - In this paper, a general class of recurrent neural networks with time-varying delays is studied. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point and the existence of periodic solutions for such delayed neural networks. Comparing with some previous literature, in which the time-varying delays were assumed to be differentiable and their derivatives were simultaneously required to be not greater than 1, the restrictions on the time-varying delays are removed. Therefore, our results obtained here improve and extend some previously related results. Finally, two numerical examples are provided to illustrate our theorems. © 2004 Elsevier Ltd. All rights reserved.

KW - Global exponential stability

KW - Neural networks

KW - Nonsingular M-matrix

KW - Periodic solutions

KW - Time-varying delays

UR - http://www.scopus.com/inward/record.url?scp=15944375785&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-15944375785&origin=recordpage

U2 - 10.1016/j.neunet.2004.11.002

DO - 10.1016/j.neunet.2004.11.002

M3 - RGC 21 - Publication in refereed journal

C2 - 15795113

SN - 0893-6080

VL - 18

SP - 161

EP - 170

JO - Neural Networks

JF - Neural Networks

IS - 2

ER -

Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays

Abstract

Research Keywords

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