Multistability of recurrent neural networks with general periodic activation functions and unbounded time-varying delays

Wang, J; Zhu, S; Ma, Q; Mu, C; Liu, X; Wen, S

Multistability of recurrent neural networks with general periodic activation functions and unbounded time-varying delays

Wang, J Zhu, S Ma, Q Mu, C Liu, X Wen, S

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Publisher:: Elsevier
Publication Type:: Journal Article
Citation:: Journal of the Franklin Institute, 2024, 361, (18), pp. 107236
Issue Date:: 2024-12-01

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Field	Value	Language
dc.contributor.author	Wang, J
dc.contributor.author	Zhu, S
dc.contributor.author	Ma, Q
dc.contributor.author	Mu, C
dc.contributor.author	Liu, X
dc.contributor.author	Wen, S https://orcid.org/0000-0001-8077-7001
dc.date.accessioned	2025-01-15T00:32:01Z
dc.date.available	2025-01-15T00:32:01Z
dc.date.issued	2024-12-01
dc.identifier.citation	Journal of the Franklin Institute, 2024, 361, (18), pp. 107236
dc.identifier.issn	0016-0032
dc.identifier.uri	http://hdl.handle.net/10453/183504
dc.description.abstract	This paper investigates the multistability of recurrent neural networks (RNNs) with unbounded time-varying delays whose activation functions are general periodic functions. The activation function can be linear, nonlinear, or have multiple corner points, as long as it satisfies Lipschitz continuous condition. According to the characteristics of the parameters of the RNNs and the state space division method, the number of equilibrium points (EPs) of the RNNs is split into three categories, which can be unique, finite, or countable infinite. Some sufficient conditions for determining the number of EPs are presented, the criterion of asymptotically stable EPs is deduced, and the attraction basins of stable EPs are estimated. Furthermore, the multistability results in this paper are an extension of some previous results. The theoretical results are validated using three numerical simulation examples.
dc.language	en
dc.publisher	Elsevier
dc.relation.ispartof	Journal of the Franklin Institute
dc.relation.isbasedon	10.1016/j.jfranklin.2024.107236
dc.rights	info:eu-repo/semantics/restrictedAccess
dc.subject	0102 Applied Mathematics, 0906 Electrical and Electronic Engineering
dc.subject.classification	Industrial Engineering & Automation
dc.subject.classification	4006 Communications engineering
dc.subject.classification	4901 Applied mathematics
dc.title	Multistability of recurrent neural networks with general periodic activation functions and unbounded time-varying delays
dc.type	Journal Article
utslib.citation.volume	361
utslib.for	0102 Applied Mathematics
utslib.for	0906 Electrical and Electronic Engineering
pubs.organisational-group	University of Technology Sydney
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	University of Technology Sydney/UTS Groups
pubs.organisational-group	University of Technology Sydney/UTS Groups/Australian Artificial Intelligence Institute (AAII)
utslib.copyright.status	in_progress	*
dc.date.updated	2025-01-15T00:31:57Z
pubs.issue	18
pubs.publication-status	Published
pubs.volume	361
utslib.citation.issue	18

Abstract:

This paper investigates the multistability of recurrent neural networks (RNNs) with unbounded time-varying delays whose activation functions are general periodic functions. The activation function can be linear, nonlinear, or have multiple corner points, as long as it satisfies Lipschitz continuous condition. According to the characteristics of the parameters of the RNNs and the state space division method, the number of equilibrium points (EPs) of the RNNs is split into three categories, which can be unique, finite, or countable infinite. Some sufficient conditions for determining the number of EPs are presented, the criterion of asymptotically stable EPs is deduced, and the attraction basins of stable EPs are estimated. Furthermore, the multistability results in this paper are an extension of some previous results. The theoretical results are validated using three numerical simulation examples.

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http://hdl.handle.net/10453/183504