Pattern Formation in a Reaction-Diffusion BAM Neural Network With Time Delay: (k1, k2) Mode Hopf-Zero Bifurcation Case
This article investigates the joint effects of connection weight and time delay on pattern formation for a delayed reaction-diffusion BAM neural network (RDBAMNN) with Neumann boundary conditions by using the ({k_{1}},{k_{2}}) mode Hopf-zero bifurcation. First, the conditions for {k_{1}} mode ze...
Gespeichert in:
| Veröffentlicht in: | IEEE transaction on neural networks and learning systems 2022-12, Vol.33 (12), p.7266-7276 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 7276 |
|---|---|
| container_issue | 12 |
| container_start_page | 7266 |
| container_title | IEEE transaction on neural networks and learning systems |
| container_volume | 33 |
| creator | Dong, Tao Xiang, Weilai Huang, Tingwen Li, Huaqing |
| description | This article investigates the joint effects of connection weight and time delay on pattern formation for a delayed reaction-diffusion BAM neural network (RDBAMNN) with Neumann boundary conditions by using the ({k_{1}},{k_{2}}) mode Hopf-zero bifurcation. First, the conditions for {k_{1}} mode zero bifurcation are obtained by choosing connection weight as the bifurcation parameter. It is found that the connection weight has a great impact on the properties of steady state. With connection weight increasing, the homogeneous steady state becomes inhomogeneous, which means that the connection weight can affect the spatial stability of steady state. Then, the specified conditions for the {k_{2}} mode Hopf bifurcation and the ({k_{1}},{k_{2}}) mode Hopf-zero bifurcation are established. By using the center manifold, the third-order normal form of the Hopf-zero bifurcation is obtained. Through the analysis of the normal form, the bifurcation diagrams on two parameters' planes (connection weight and time delay) are obtained, which contains six areas. Some interesting spatial patterns are found in these areas: a homogeneous periodic solution, a homogeneous steady state, two inhomogeneous steady state, and two inhomogeneous periodic solutions. |
| doi_str_mv | 10.1109/TNNLS.2021.3084693 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_crossref_primary_10_1109_TNNLS_2021_3084693</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>9451545</ieee_id><sourcerecordid>2742703957</sourcerecordid><originalsourceid>FETCH-LOGICAL-c258t-dbd458358d4dabd276799f89d889a00ff9ab7f8dda36f1556539e981a97e1fa23</originalsourceid><addsrcrecordid>eNpdkUtPGzEUha2qqCDgD8DGEhsqMamfM3Z3EKBUCimCoFZsLGd8LUwm49SeAfHvOyGIRe_mPnTO0ZU-hA4oGVFK9LfZdDq5GzHC6IgTJUrNP6EdRktWMK7U54-5-rON9nN-IkOVRJZCf0HbXNAhhJQ76PnGdh2kFl_GtLRdiC0OLbb4Fmy93orz4H2f1_ez02s8hT7ZZmjdS0wL_Dt0j3gWloDPobGv3_Hxgp7gBfuKr6MDfBVXvniAFPFZ8H2qN_ljm2EPbXnbZNh_77vo_vJiNr4qJr9-_ByfToqaSdUVbu6EVFwqJ5ydO1aVldZeaaeUtoR4r-288so5y0tPpSwl16AVtboC6i3ju-h4k7tK8W8PuTPLkGtoGttC7LNhUhBJtSB0kB79J32KfWqH7wyrBKsI17IaVGyjqlPMOYE3qxSWNr0aSswajHkDY9ZgzDuYwXS4MQUA-DBoIakUkv8DrRWFtg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2742703957</pqid></control><display><type>article</type><title>Pattern Formation in a Reaction-Diffusion BAM Neural Network With Time Delay: (k1, k2) Mode Hopf-Zero Bifurcation Case</title><source>IEEE Electronic Library (IEL)</source><creator>Dong, Tao ; Xiang, Weilai ; Huang, Tingwen ; Li, Huaqing</creator><creatorcontrib>Dong, Tao ; Xiang, Weilai ; Huang, Tingwen ; Li, Huaqing</creatorcontrib><description><![CDATA[This article investigates the joint effects of connection weight and time delay on pattern formation for a delayed reaction-diffusion BAM neural network (RDBAMNN) with Neumann boundary conditions by using the <inline-formula> <tex-math notation="LaTeX">({k_{1}},{k_{2}}) </tex-math></inline-formula> mode Hopf-zero bifurcation. First, the conditions for <inline-formula> <tex-math notation="LaTeX">{k_{1}} </tex-math></inline-formula> mode zero bifurcation are obtained by choosing connection weight as the bifurcation parameter. It is found that the connection weight has a great impact on the properties of steady state. With connection weight increasing, the homogeneous steady state becomes inhomogeneous, which means that the connection weight can affect the spatial stability of steady state. Then, the specified conditions for the <inline-formula> <tex-math notation="LaTeX">{k_{2}} </tex-math></inline-formula> mode Hopf bifurcation and the <inline-formula> <tex-math notation="LaTeX">({k_{1}},{k_{2}}) </tex-math></inline-formula> mode Hopf-zero bifurcation are established. By using the center manifold, the third-order normal form of the Hopf-zero bifurcation is obtained. Through the analysis of the normal form, the bifurcation diagrams on two parameters' planes (connection weight and time delay) are obtained, which contains six areas. Some interesting spatial patterns are found in these areas: a homogeneous periodic solution, a homogeneous steady state, two inhomogeneous steady state, and two inhomogeneous periodic solutions.]]></description><identifier>ISSN: 2162-237X</identifier><identifier>EISSN: 2162-2388</identifier><identifier>DOI: 10.1109/TNNLS.2021.3084693</identifier><identifier>PMID: 34111006</identifier><identifier>CODEN: ITNNAL</identifier><language>eng</language><publisher>Piscataway: IEEE</publisher><subject>Bifurcation ; Boundary conditions ; Canonical forms ; Center manifold ; Delay effects ; Diffusion ; Hopf bifurcation ; Hopf-zero bifurcation ; Neural networks ; Neurons ; Nonhomogeneous media ; Parameters ; Pattern formation ; reaction-diffusion BAM neural network (RDBAMNN) ; Recurrent neural networks ; spatial patterns ; Steady state ; Time lag</subject><ispartof>IEEE transaction on neural networks and learning systems, 2022-12, Vol.33 (12), p.7266-7276</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2022</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c258t-dbd458358d4dabd276799f89d889a00ff9ab7f8dda36f1556539e981a97e1fa23</citedby><cites>FETCH-LOGICAL-c258t-dbd458358d4dabd276799f89d889a00ff9ab7f8dda36f1556539e981a97e1fa23</cites><orcidid>0000-0001-6310-8965 ; 0000-0003-0555-2720 ; 0000-0001-9610-846X ; 0000-0002-0067-5329</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/9451545$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/9451545$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Dong, Tao</creatorcontrib><creatorcontrib>Xiang, Weilai</creatorcontrib><creatorcontrib>Huang, Tingwen</creatorcontrib><creatorcontrib>Li, Huaqing</creatorcontrib><title>Pattern Formation in a Reaction-Diffusion BAM Neural Network With Time Delay: (k1, k2) Mode Hopf-Zero Bifurcation Case</title><title>IEEE transaction on neural networks and learning systems</title><addtitle>TNNLS</addtitle><description><![CDATA[This article investigates the joint effects of connection weight and time delay on pattern formation for a delayed reaction-diffusion BAM neural network (RDBAMNN) with Neumann boundary conditions by using the <inline-formula> <tex-math notation="LaTeX">({k_{1}},{k_{2}}) </tex-math></inline-formula> mode Hopf-zero bifurcation. First, the conditions for <inline-formula> <tex-math notation="LaTeX">{k_{1}} </tex-math></inline-formula> mode zero bifurcation are obtained by choosing connection weight as the bifurcation parameter. It is found that the connection weight has a great impact on the properties of steady state. With connection weight increasing, the homogeneous steady state becomes inhomogeneous, which means that the connection weight can affect the spatial stability of steady state. Then, the specified conditions for the <inline-formula> <tex-math notation="LaTeX">{k_{2}} </tex-math></inline-formula> mode Hopf bifurcation and the <inline-formula> <tex-math notation="LaTeX">({k_{1}},{k_{2}}) </tex-math></inline-formula> mode Hopf-zero bifurcation are established. By using the center manifold, the third-order normal form of the Hopf-zero bifurcation is obtained. Through the analysis of the normal form, the bifurcation diagrams on two parameters' planes (connection weight and time delay) are obtained, which contains six areas. Some interesting spatial patterns are found in these areas: a homogeneous periodic solution, a homogeneous steady state, two inhomogeneous steady state, and two inhomogeneous periodic solutions.]]></description><subject>Bifurcation</subject><subject>Boundary conditions</subject><subject>Canonical forms</subject><subject>Center manifold</subject><subject>Delay effects</subject><subject>Diffusion</subject><subject>Hopf bifurcation</subject><subject>Hopf-zero bifurcation</subject><subject>Neural networks</subject><subject>Neurons</subject><subject>Nonhomogeneous media</subject><subject>Parameters</subject><subject>Pattern formation</subject><subject>reaction-diffusion BAM neural network (RDBAMNN)</subject><subject>Recurrent neural networks</subject><subject>spatial patterns</subject><subject>Steady state</subject><subject>Time lag</subject><issn>2162-237X</issn><issn>2162-2388</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkUtPGzEUha2qqCDgD8DGEhsqMamfM3Z3EKBUCimCoFZsLGd8LUwm49SeAfHvOyGIRe_mPnTO0ZU-hA4oGVFK9LfZdDq5GzHC6IgTJUrNP6EdRktWMK7U54-5-rON9nN-IkOVRJZCf0HbXNAhhJQ76PnGdh2kFl_GtLRdiC0OLbb4Fmy93orz4H2f1_ez02s8hT7ZZmjdS0wL_Dt0j3gWloDPobGv3_Hxgp7gBfuKr6MDfBVXvniAFPFZ8H2qN_ljm2EPbXnbZNh_77vo_vJiNr4qJr9-_ByfToqaSdUVbu6EVFwqJ5ydO1aVldZeaaeUtoR4r-288so5y0tPpSwl16AVtboC6i3ju-h4k7tK8W8PuTPLkGtoGttC7LNhUhBJtSB0kB79J32KfWqH7wyrBKsI17IaVGyjqlPMOYE3qxSWNr0aSswajHkDY9ZgzDuYwXS4MQUA-DBoIakUkv8DrRWFtg</recordid><startdate>20221201</startdate><enddate>20221201</enddate><creator>Dong, Tao</creator><creator>Xiang, Weilai</creator><creator>Huang, Tingwen</creator><creator>Li, Huaqing</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QF</scope><scope>7QO</scope><scope>7QP</scope><scope>7QQ</scope><scope>7QR</scope><scope>7SC</scope><scope>7SE</scope><scope>7SP</scope><scope>7SR</scope><scope>7TA</scope><scope>7TB</scope><scope>7TK</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>H8D</scope><scope>JG9</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>P64</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0001-6310-8965</orcidid><orcidid>https://orcid.org/0000-0003-0555-2720</orcidid><orcidid>https://orcid.org/0000-0001-9610-846X</orcidid><orcidid>https://orcid.org/0000-0002-0067-5329</orcidid></search><sort><creationdate>20221201</creationdate><title>Pattern Formation in a Reaction-Diffusion BAM Neural Network With Time Delay: (k1, k2) Mode Hopf-Zero Bifurcation Case</title><author>Dong, Tao ; Xiang, Weilai ; Huang, Tingwen ; Li, Huaqing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c258t-dbd458358d4dabd276799f89d889a00ff9ab7f8dda36f1556539e981a97e1fa23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Bifurcation</topic><topic>Boundary conditions</topic><topic>Canonical forms</topic><topic>Center manifold</topic><topic>Delay effects</topic><topic>Diffusion</topic><topic>Hopf bifurcation</topic><topic>Hopf-zero bifurcation</topic><topic>Neural networks</topic><topic>Neurons</topic><topic>Nonhomogeneous media</topic><topic>Parameters</topic><topic>Pattern formation</topic><topic>reaction-diffusion BAM neural network (RDBAMNN)</topic><topic>Recurrent neural networks</topic><topic>spatial patterns</topic><topic>Steady state</topic><topic>Time lag</topic><toplevel>online_resources</toplevel><creatorcontrib>Dong, Tao</creatorcontrib><creatorcontrib>Xiang, Weilai</creatorcontrib><creatorcontrib>Huang, Tingwen</creatorcontrib><creatorcontrib>Li, Huaqing</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Aluminium Industry Abstracts</collection><collection>Biotechnology Research Abstracts</collection><collection>Calcium & Calcified Tissue Abstracts</collection><collection>Ceramic Abstracts</collection><collection>Chemoreception Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Corrosion Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Neurosciences Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>MEDLINE - Academic</collection><jtitle>IEEE transaction on neural networks and learning systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Dong, Tao</au><au>Xiang, Weilai</au><au>Huang, Tingwen</au><au>Li, Huaqing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Pattern Formation in a Reaction-Diffusion BAM Neural Network With Time Delay: (k1, k2) Mode Hopf-Zero Bifurcation Case</atitle><jtitle>IEEE transaction on neural networks and learning systems</jtitle><stitle>TNNLS</stitle><date>2022-12-01</date><risdate>2022</risdate><volume>33</volume><issue>12</issue><spage>7266</spage><epage>7276</epage><pages>7266-7276</pages><issn>2162-237X</issn><eissn>2162-2388</eissn><coden>ITNNAL</coden><abstract><![CDATA[This article investigates the joint effects of connection weight and time delay on pattern formation for a delayed reaction-diffusion BAM neural network (RDBAMNN) with Neumann boundary conditions by using the <inline-formula> <tex-math notation="LaTeX">({k_{1}},{k_{2}}) </tex-math></inline-formula> mode Hopf-zero bifurcation. First, the conditions for <inline-formula> <tex-math notation="LaTeX">{k_{1}} </tex-math></inline-formula> mode zero bifurcation are obtained by choosing connection weight as the bifurcation parameter. It is found that the connection weight has a great impact on the properties of steady state. With connection weight increasing, the homogeneous steady state becomes inhomogeneous, which means that the connection weight can affect the spatial stability of steady state. Then, the specified conditions for the <inline-formula> <tex-math notation="LaTeX">{k_{2}} </tex-math></inline-formula> mode Hopf bifurcation and the <inline-formula> <tex-math notation="LaTeX">({k_{1}},{k_{2}}) </tex-math></inline-formula> mode Hopf-zero bifurcation are established. By using the center manifold, the third-order normal form of the Hopf-zero bifurcation is obtained. Through the analysis of the normal form, the bifurcation diagrams on two parameters' planes (connection weight and time delay) are obtained, which contains six areas. Some interesting spatial patterns are found in these areas: a homogeneous periodic solution, a homogeneous steady state, two inhomogeneous steady state, and two inhomogeneous periodic solutions.]]></abstract><cop>Piscataway</cop><pub>IEEE</pub><pmid>34111006</pmid><doi>10.1109/TNNLS.2021.3084693</doi><tpages>11</tpages><orcidid>https://orcid.org/0000-0001-6310-8965</orcidid><orcidid>https://orcid.org/0000-0003-0555-2720</orcidid><orcidid>https://orcid.org/0000-0001-9610-846X</orcidid><orcidid>https://orcid.org/0000-0002-0067-5329</orcidid></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 2162-237X |
| ispartof | IEEE transaction on neural networks and learning systems, 2022-12, Vol.33 (12), p.7266-7276 |
| issn | 2162-237X 2162-2388 |
| language | eng |
| recordid | cdi_crossref_primary_10_1109_TNNLS_2021_3084693 |
| source | IEEE Electronic Library (IEL) |
| subjects | Bifurcation Boundary conditions Canonical forms Center manifold Delay effects Diffusion Hopf bifurcation Hopf-zero bifurcation Neural networks Neurons Nonhomogeneous media Parameters Pattern formation reaction-diffusion BAM neural network (RDBAMNN) Recurrent neural networks spatial patterns Steady state Time lag |
| title | Pattern Formation in a Reaction-Diffusion BAM Neural Network With Time Delay: (k1, k2) Mode Hopf-Zero Bifurcation Case |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-08T18%3A01%3A37IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Pattern%20Formation%20in%20a%20Reaction-Diffusion%20BAM%20Neural%20Network%20With%20Time%20Delay:%20(k1,%20k2)%20Mode%20Hopf-Zero%20Bifurcation%20Case&rft.jtitle=IEEE%20transaction%20on%20neural%20networks%20and%20learning%20systems&rft.au=Dong,%20Tao&rft.date=2022-12-01&rft.volume=33&rft.issue=12&rft.spage=7266&rft.epage=7276&rft.pages=7266-7276&rft.issn=2162-237X&rft.eissn=2162-2388&rft.coden=ITNNAL&rft_id=info:doi/10.1109/TNNLS.2021.3084693&rft_dat=%3Cproquest_RIE%3E2742703957%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2742703957&rft_id=info:pmid/34111006&rft_ieee_id=9451545&rfr_iscdi=true |