Generalized norm for existence, uniqueness and stability of Hopfield neural networks with discrete and distributed delays.

Wang, H; Wei, G; Wen, S; Huang, T

Generalized norm for existence, uniqueness and stability of Hopfield neural networks with discrete and distributed delays.

Wang, H Wei, G Wen, S

Huang, T

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Publisher:: Elsevier BV
Publication Type:: Journal Article
Citation:: Neural networks : the official journal of the International Neural Network Society, 2020, 128, pp. 288-293
Issue Date:: 2020-08

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Field	Value	Language
dc.contributor.author	Wang, H
dc.contributor.author	Wei, G
dc.contributor.author	Wen, S https://orcid.org/0000-0002-5048-0319
dc.contributor.author	Huang, T
dc.date.accessioned	2021-01-11T00:41:35Z
dc.date.available	2020-05-11
dc.date.available	2021-01-11T00:41:35Z
dc.date.issued	2020-08
dc.identifier.citation	Neural networks : the official journal of the International Neural Network Society, 2020, 128, pp. 288-293
dc.identifier.issn	0893-6080
dc.identifier.issn	1879-2782
dc.identifier.uri	http://hdl.handle.net/10453/145265
dc.description.abstract	In this paper, the existence, uniqueness and stability criteria of solutions for Hopfield neural networks with discrete and distributed delays (DDD HNNs) are investigated by the definitions of three kinds of generalized norm (ξ-norm). A general DDD HNN model is firstly introduced, where the discrete delays τpq(t) are asynchronous time-varying delays. Then, {ξ,1}-norm, {ξ,2}-norm and {ξ,∞}-norm are successively used to derive the existence, uniqueness and stability criteria of solutions for the DDD HNNs. In the proof of theorems, special functions and assumptions are given to deal with discrete and distributed delays. Furthermore, a corollary is concluded for the existence and stability criteria of solutions. The methods given in this paper can also be used to study the synchronization and μ-stability of different DDD NNs. Finally, two numerical examples and their simulation figures are given to illustrate the effectiveness of these results.
dc.format	Print-Electronic
dc.language	eng
dc.publisher	Elsevier BV
dc.relation.ispartof	Neural networks : the official journal of the International Neural Network Society
dc.relation.isbasedon	10.1016/j.neunet.2020.05.014
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject.classification	Artificial Intelligence & Image Processing
dc.subject.mesh	Time Factors
dc.subject.mesh	Neural Networks, Computer
dc.subject.mesh	Neural Networks, Computer
dc.subject.mesh	Time Factors
dc.title	Generalized norm for existence, uniqueness and stability of Hopfield neural networks with discrete and distributed delays.
dc.type	Journal Article
utslib.citation.volume	128
utslib.location.activity	United States
utslib.for	0801 Artificial Intelligence and Image Processing
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - AAII - Australian Artificial Intelligence Institute
pubs.organisational-group	/University of Technology Sydney
utslib.copyright.status	closed_access	*
dc.date.updated	2021-01-11T00:41:11Z
pubs.publication-status	Published
pubs.volume	128

Abstract:

In this paper, the existence, uniqueness and stability criteria of solutions for Hopfield neural networks with discrete and distributed delays (DDD HNNs) are investigated by the definitions of three kinds of generalized norm (ξ-norm). A general DDD HNN model is firstly introduced, where the discrete delays τpq(t) are asynchronous time-varying delays. Then, {ξ,1}-norm, {ξ,2}-norm and {ξ,∞}-norm are successively used to derive the existence, uniqueness and stability criteria of solutions for the DDD HNNs. In the proof of theorems, special functions and assumptions are given to deal with discrete and distributed delays. Furthermore, a corollary is concluded for the existence and stability criteria of solutions. The methods given in this paper can also be used to study the synchronization and μ-stability of different DDD NNs. Finally, two numerical examples and their simulation figures are given to illustrate the effectiveness of these results.

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http://hdl.handle.net/10453/145265