Multistability of Quaternion-Valued Recurrent Neural Networks with Discontinuous Nonmonotonic Piecewise Nonlinear Activation Functions
In this article, the coexistence and dynamical behaviors of multiple equilibrium points for quaternion-valued neural networks (QVNNs) are investigated, whose activation functions are discontinuous and nonmonotonic piecewise nonlinear. According to the Hamilton rules, the QVNNs can be divided into fo...
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| Veröffentlicht in: | Neural processing letters 2023-10, Vol.55 (5), p.5855-5884 |
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| creator | Du, Weihao Xiang, Jianglian Tan, Manchun |
| description | In this article, the coexistence and dynamical behaviors of multiple equilibrium points for quaternion-valued neural networks (QVNNs) are investigated, whose activation functions are discontinuous and nonmonotonic piecewise nonlinear. According to the Hamilton rules, the QVNNs can be divided into four real-valued parts. By utilizing the Brouwer’s Fixed Point Theorem and property of strictly diagonally dominant matrices, some sufficient conditions are derived to ensure that the QVNNs have at least
5
4
n
equilibrium points,
3
4
n
of them are locally exponentially stable, and the others are unstable. It is shown that the number of stable equilibria in QVNNs is more than that in the real-valued ones. Finally, a numerical simulation is presented to clarify the theoretical analysis is valid. |
| doi_str_mv | 10.1007/s11063-022-11116-w |
| format | Article |
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5
4
n
equilibrium points,
3
4
n
of them are locally exponentially stable, and the others are unstable. It is shown that the number of stable equilibria in QVNNs is more than that in the real-valued ones. Finally, a numerical simulation is presented to clarify the theoretical analysis is valid.</description><identifier>ISSN: 1370-4621</identifier><identifier>EISSN: 1573-773X</identifier><identifier>DOI: 10.1007/s11063-022-11116-w</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Artificial Intelligence ; Complex Systems ; Computational Intelligence ; Computer Science ; Eigenvalues ; Equilibrium ; Fixed points (mathematics) ; Mathematical functions ; Neural networks ; Quaternions ; Recurrent neural networks</subject><ispartof>Neural processing letters, 2023-10, Vol.55 (5), p.5855-5884</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-2728aee3b5e1288321a087efc8a3602e15867cfe39d8b2860062cb7efb440afe3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11063-022-11116-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918349582?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,776,780,21367,27901,27902,33721,41464,42533,43781,51294</link.rule.ids></links><search><creatorcontrib>Du, Weihao</creatorcontrib><creatorcontrib>Xiang, Jianglian</creatorcontrib><creatorcontrib>Tan, Manchun</creatorcontrib><title>Multistability of Quaternion-Valued Recurrent Neural Networks with Discontinuous Nonmonotonic Piecewise Nonlinear Activation Functions</title><title>Neural processing letters</title><addtitle>Neural Process Lett</addtitle><description>In this article, the coexistence and dynamical behaviors of multiple equilibrium points for quaternion-valued neural networks (QVNNs) are investigated, whose activation functions are discontinuous and nonmonotonic piecewise nonlinear. According to the Hamilton rules, the QVNNs can be divided into four real-valued parts. By utilizing the Brouwer’s Fixed Point Theorem and property of strictly diagonally dominant matrices, some sufficient conditions are derived to ensure that the QVNNs have at least
5
4
n
equilibrium points,
3
4
n
of them are locally exponentially stable, and the others are unstable. It is shown that the number of stable equilibria in QVNNs is more than that in the real-valued ones. Finally, a numerical simulation is presented to clarify the theoretical analysis is valid.</description><subject>Artificial Intelligence</subject><subject>Complex Systems</subject><subject>Computational Intelligence</subject><subject>Computer Science</subject><subject>Eigenvalues</subject><subject>Equilibrium</subject><subject>Fixed points (mathematics)</subject><subject>Mathematical functions</subject><subject>Neural networks</subject><subject>Quaternions</subject><subject>Recurrent neural networks</subject><issn>1370-4621</issn><issn>1573-773X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp9UMtKQzEUvIiCtfoDrgKuo3m0N-my-AbfqLgLuem5mnpNNA8v_QG_29QK7jybGYaZOTBVtUvJPiVEHERKSc0xYQzTcjXu16oBHQuOheBP64VzQfCoZnSz2opxTkiJMTKovi5zl2xMurGdTQvkW3SbdYLgrHf4UXcZZugOTA4BXEJXkIPuCqTeh9eIepte0JGNxrtkXfY5oivv3rzzyTtr0I0FA72NsJQ760AHNDXJfupU-tFJdmZJ4na10eouws4vDquHk-P7wzN8cX16fji9wIYJkjATTGoA3oyBMik5o5pIAa2RmteEAR3LWpgW-GQmGyZrQmpmmmJoRiOiiz6s9la978F_ZIhJzX0OrrxUbEIlH03GkhUXW7lM8DEGaNV7sG86LBQlarm3Wu2tyt7qZ2_VlxBfhWIxu2cIf9X_pL4BWP2Hfw</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Du, Weihao</creator><creator>Xiang, Jianglian</creator><creator>Tan, Manchun</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PSYQQ</scope></search><sort><creationdate>20231001</creationdate><title>Multistability of Quaternion-Valued Recurrent Neural Networks with Discontinuous Nonmonotonic Piecewise Nonlinear Activation Functions</title><author>Du, Weihao ; Xiang, Jianglian ; Tan, Manchun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-2728aee3b5e1288321a087efc8a3602e15867cfe39d8b2860062cb7efb440afe3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Artificial Intelligence</topic><topic>Complex Systems</topic><topic>Computational Intelligence</topic><topic>Computer Science</topic><topic>Eigenvalues</topic><topic>Equilibrium</topic><topic>Fixed points (mathematics)</topic><topic>Mathematical functions</topic><topic>Neural networks</topic><topic>Quaternions</topic><topic>Recurrent neural networks</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Du, Weihao</creatorcontrib><creatorcontrib>Xiang, Jianglian</creatorcontrib><creatorcontrib>Tan, Manchun</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest One Psychology</collection><jtitle>Neural processing letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Du, Weihao</au><au>Xiang, Jianglian</au><au>Tan, Manchun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multistability of Quaternion-Valued Recurrent Neural Networks with Discontinuous Nonmonotonic Piecewise Nonlinear Activation Functions</atitle><jtitle>Neural processing letters</jtitle><stitle>Neural Process Lett</stitle><date>2023-10-01</date><risdate>2023</risdate><volume>55</volume><issue>5</issue><spage>5855</spage><epage>5884</epage><pages>5855-5884</pages><issn>1370-4621</issn><eissn>1573-773X</eissn><abstract>In this article, the coexistence and dynamical behaviors of multiple equilibrium points for quaternion-valued neural networks (QVNNs) are investigated, whose activation functions are discontinuous and nonmonotonic piecewise nonlinear. 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5
4
n
equilibrium points,
3
4
n
of them are locally exponentially stable, and the others are unstable. It is shown that the number of stable equilibria in QVNNs is more than that in the real-valued ones. Finally, a numerical simulation is presented to clarify the theoretical analysis is valid.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11063-022-11116-w</doi><tpages>30</tpages></addata></record> |
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| subjects | Artificial Intelligence Complex Systems Computational Intelligence Computer Science Eigenvalues Equilibrium Fixed points (mathematics) Mathematical functions Neural networks Quaternions Recurrent neural networks |
| title | Multistability of Quaternion-Valued Recurrent Neural Networks with Discontinuous Nonmonotonic Piecewise Nonlinear Activation Functions |
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