Logistic Equation with Long Delay Feedback
We study the local dynamics of the delay logistic equation with an additional feedback containing a large delay. Critical cases in the problem of stability of the zero equilibrium state are identified, and it is shown that they are infinite-dimensional. The well-known methods for studying local dyna...
Gespeichert in:
| Veröffentlicht in: | Differential equations 2024, Vol.60 (2), p.145-151 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 151 |
|---|---|
| container_issue | 2 |
| container_start_page | 145 |
| container_title | Differential equations |
| container_volume | 60 |
| creator | Kashchenko, S. A. |
| description | We study the local dynamics of the delay logistic equation with an additional feedback containing a large delay. Critical cases in the problem of stability of the zero equilibrium state are identified, and it is shown that they are infinite-dimensional. The well-known methods for studying local dynamics based on the theory of invariant integral manifolds and normal forms do not apply here. The methods of infinite-dimensional normalization proposed by the author are used and developed. As the main results, special nonlinear boundary value problems of parabolic type are constructed, which play the role of normal forms. They determine the leading terms of the asymptotic expansions of solutions of the original equation and are called quasinormal forms. |
| doi_str_mv | 10.1134/S0012266124020010 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_sprin</sourceid><recordid>TN_cdi_proquest_journals_3064983574</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3064983574</sourcerecordid><originalsourceid>FETCH-LOGICAL-p156t-a30921e0457700e0b95c91bb9cd2009edcb8de0d7beda18ef379436d789324763</originalsourceid><addsrcrecordid>eNplkE9Lw0AQxRdRMFY_gLeANyE6s7vZP0eprQoBD-o5ZLPTmFqSNJsgfvsmVPDgaR68H-8Nj7FrhDtEIe_fAJBzpZBL4JOGExahApMIMOKURbOdzP45uwhhCwBWYxqx26yt6jDUZbzaj8VQt038XQ-fcdY2VfxIu-InXhN5V5Rfl-xsU-wCXf3eBftYr96Xz0n2-vSyfMiSDlM1JIUAy5FAploDEDiblhads6WfHrPkS2c8gdeOfIGGNkJbKZTXxgoutRILdnPM7fp2P1IY8m079s1UmQtQ0hqRajlR_EiFrq-bivo_CiGfN8n_bSIOx7RRSw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3064983574</pqid></control><display><type>article</type><title>Logistic Equation with Long Delay Feedback</title><source>SpringerLink Journals - AutoHoldings</source><creator>Kashchenko, S. A.</creator><creatorcontrib>Kashchenko, S. A.</creatorcontrib><description>We study the local dynamics of the delay logistic equation with an additional feedback containing a large delay. Critical cases in the problem of stability of the zero equilibrium state are identified, and it is shown that they are infinite-dimensional. The well-known methods for studying local dynamics based on the theory of invariant integral manifolds and normal forms do not apply here. The methods of infinite-dimensional normalization proposed by the author are used and developed. As the main results, special nonlinear boundary value problems of parabolic type are constructed, which play the role of normal forms. They determine the leading terms of the asymptotic expansions of solutions of the original equation and are called quasinormal forms.</description><identifier>ISSN: 0012-2661</identifier><identifier>EISSN: 1608-3083</identifier><identifier>DOI: 10.1134/S0012266124020010</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Asymptotic series ; Boundary value problems ; Delay ; Difference and Functional Equations ; Feedback ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Partial Differential Equations</subject><ispartof>Differential equations, 2024, Vol.60 (2), p.145-151</ispartof><rights>Pleiades Publishing, Ltd. 2024</rights><rights>Pleiades Publishing, Ltd. 2024.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p156t-a30921e0457700e0b95c91bb9cd2009edcb8de0d7beda18ef379436d789324763</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0012266124020010$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0012266124020010$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Kashchenko, S. A.</creatorcontrib><title>Logistic Equation with Long Delay Feedback</title><title>Differential equations</title><addtitle>Diff Equat</addtitle><description>We study the local dynamics of the delay logistic equation with an additional feedback containing a large delay. Critical cases in the problem of stability of the zero equilibrium state are identified, and it is shown that they are infinite-dimensional. The well-known methods for studying local dynamics based on the theory of invariant integral manifolds and normal forms do not apply here. The methods of infinite-dimensional normalization proposed by the author are used and developed. As the main results, special nonlinear boundary value problems of parabolic type are constructed, which play the role of normal forms. They determine the leading terms of the asymptotic expansions of solutions of the original equation and are called quasinormal forms.</description><subject>Asymptotic series</subject><subject>Boundary value problems</subject><subject>Delay</subject><subject>Difference and Functional Equations</subject><subject>Feedback</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><issn>0012-2661</issn><issn>1608-3083</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNplkE9Lw0AQxRdRMFY_gLeANyE6s7vZP0eprQoBD-o5ZLPTmFqSNJsgfvsmVPDgaR68H-8Nj7FrhDtEIe_fAJBzpZBL4JOGExahApMIMOKURbOdzP45uwhhCwBWYxqx26yt6jDUZbzaj8VQt038XQ-fcdY2VfxIu-InXhN5V5Rfl-xsU-wCXf3eBftYr96Xz0n2-vSyfMiSDlM1JIUAy5FAploDEDiblhads6WfHrPkS2c8gdeOfIGGNkJbKZTXxgoutRILdnPM7fp2P1IY8m079s1UmQtQ0hqRajlR_EiFrq-bivo_CiGfN8n_bSIOx7RRSw</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Kashchenko, S. A.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2024</creationdate><title>Logistic Equation with Long Delay Feedback</title><author>Kashchenko, S. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p156t-a30921e0457700e0b95c91bb9cd2009edcb8de0d7beda18ef379436d789324763</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Asymptotic series</topic><topic>Boundary value problems</topic><topic>Delay</topic><topic>Difference and Functional Equations</topic><topic>Feedback</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kashchenko, S. A.</creatorcontrib><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering 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><jtitle>Differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kashchenko, S. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Logistic Equation with Long Delay Feedback</atitle><jtitle>Differential equations</jtitle><stitle>Diff Equat</stitle><date>2024</date><risdate>2024</risdate><volume>60</volume><issue>2</issue><spage>145</spage><epage>151</epage><pages>145-151</pages><issn>0012-2661</issn><eissn>1608-3083</eissn><abstract>We study the local dynamics of the delay logistic equation with an additional feedback containing a large delay. Critical cases in the problem of stability of the zero equilibrium state are identified, and it is shown that they are infinite-dimensional. The well-known methods for studying local dynamics based on the theory of invariant integral manifolds and normal forms do not apply here. The methods of infinite-dimensional normalization proposed by the author are used and developed. As the main results, special nonlinear boundary value problems of parabolic type are constructed, which play the role of normal forms. They determine the leading terms of the asymptotic expansions of solutions of the original equation and are called quasinormal forms.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0012266124020010</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0012-2661 |
| ispartof | Differential equations, 2024, Vol.60 (2), p.145-151 |
| issn | 0012-2661 1608-3083 |
| language | eng |
| recordid | cdi_proquest_journals_3064983574 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Asymptotic series Boundary value problems Delay Difference and Functional Equations Feedback Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations |
| title | Logistic Equation with Long Delay Feedback |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T18%3A08%3A27IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_sprin&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Logistic%20Equation%20with%20Long%20Delay%20Feedback&rft.jtitle=Differential%20equations&rft.au=Kashchenko,%20S.%20A.&rft.date=2024&rft.volume=60&rft.issue=2&rft.spage=145&rft.epage=151&rft.pages=145-151&rft.issn=0012-2661&rft.eissn=1608-3083&rft_id=info:doi/10.1134/S0012266124020010&rft_dat=%3Cproquest_sprin%3E3064983574%3C/proquest_sprin%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3064983574&rft_id=info:pmid/&rfr_iscdi=true |