Multistability of Complex-Valued NNs With General Periodic-Type Activation Functions and Its Application to Associative Memories

Zhao, Q; Zhu, S; Mu, C; Liu, X; Wen, S

Multistability of Complex-Valued NNs With General Periodic-Type Activation Functions and Its Application to Associative Memories

Zhao, Q Zhu, S Mu, C Liu, X Wen, S

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Publisher:: Institute of Electrical and Electronics Engineers (IEEE)
Publication Type:: Journal Article
Citation:: IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2024, 54, (6), pp. 3749-3761
Issue Date:: 2024-06-01

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Field	Value	Language
dc.contributor.author	Zhao, Q
dc.contributor.author	Zhu, S
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	2024-08-07T05:18:49Z
dc.date.available	2024-08-07T05:18:49Z
dc.date.issued	2024-06-01
dc.identifier.citation	IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2024, 54, (6), pp. 3749-3761
dc.identifier.issn	2168-2216
dc.identifier.issn	2168-2232
dc.identifier.uri	http://hdl.handle.net/10453/180296
dc.description.abstract	This article mainly studies the multistability of complex-valued neural networks (CVNNs) with general periodic-type activation functions. In order to improve the storage capacity of associative memory, a general periodic-type activation function is introduced which obtains three different numbers of equilibrium points (EPs), including unique, finite, and countable infinite. The existence and stability of equilibria are investigated based on Brouwer's fixed point theorem and {M} -matrix method. By means of a sign function on complex numbers, stability is confirmed using a new norm on the absolute values of the real and imaginary parts. The attraction basins of exponentially stable equilibria are estimated, which are bigger than the subspaces of the original division. Also, the design of associative memory is given. Finally, two numerical simulation examples verify the obtained results.
dc.language	en
dc.publisher	Institute of Electrical and Electronics Engineers (IEEE)
dc.relation.ispartof	IEEE Transactions on Systems, Man, and Cybernetics: Systems
dc.relation.isbasedon	10.1109/TSMC.2024.3371164
dc.rights	info:eu-repo/semantics/restrictedAccess
dc.title	Multistability of Complex-Valued NNs With General Periodic-Type Activation Functions and Its Application to Associative Memories
dc.type	Journal Article
utslib.citation.volume	54
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/Strength - AAII - Australian Artificial Intelligence Institute
pubs.organisational-group	University of Technology Sydney/All Manual Groups
pubs.organisational-group	University of Technology Sydney/All Manual Groups/Australian Artificial Intelligence Institute (AAII)
utslib.copyright.status	in_progress	*
dc.date.updated	2024-08-07T05:18:47Z
pubs.issue	6
pubs.publication-status	Published
pubs.volume	54
utslib.citation.issue	6

Abstract:

This article mainly studies the multistability of complex-valued neural networks (CVNNs) with general periodic-type activation functions. In order to improve the storage capacity of associative memory, a general periodic-type activation function is introduced which obtains three different numbers of equilibrium points (EPs), including unique, finite, and countable infinite. The existence and stability of equilibria are investigated based on Brouwer's fixed point theorem and {M} -matrix method. By means of a sign function on complex numbers, stability is confirmed using a new norm on the absolute values of the real and imaginary parts. The attraction basins of exponentially stable equilibria are estimated, which are bigger than the subspaces of the original division. Also, the design of associative memory is given. Finally, two numerical simulation examples verify the obtained results.

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http://hdl.handle.net/10453/180296