On Limit Cycles of Autonomous Systems
We consider the problem of the existence of limit cycles for autonomous systems of differential equations. We present quite elementary considerations that can be useful in discussing qualitative issues that arise in the course of ordinary differential equations. We establish that any simple closed c...
Gespeichert in:
| Veröffentlicht in: | Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.286 (1), p.68-88 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 88 |
|---|---|
| container_issue | 1 |
| container_start_page | 68 |
| container_title | Journal of mathematical sciences (New York, N.Y.) |
| container_volume | 286 |
| creator | Ivanova, T. M. Kostin, A. B. Rubinshtein, A. I. Sherstyukov, V. B. |
| description | We consider the problem of the existence of limit cycles for autonomous systems of differential equations. We present quite elementary considerations that can be useful in discussing qualitative issues that arise in the course of ordinary differential equations. We establish that any simple closed curve defined by the equation
F
(
x
,
y
) = 1 with a sufficiently general function
F
is a limit cycle for the corresponding autonomous system on the plane (and even for an infinite number of systems depending on the real parameter). These systems are written out explicitly. We analyze in detail several specific examples. Graphic illustrations are provided. |
| doi_str_mv | 10.1007/s10958-024-07491-5 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_sprin</sourceid><recordid>TN_cdi_proquest_journals_3144359571</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3144359571</sourcerecordid><originalsourceid>FETCH-LOGICAL-p725-1379f3548b2aded3b733b56cb12893a2fd7203d61ead142f843292f4164f00813</originalsourceid><addsrcrecordid>eNpFkEtLxDAUhYMoOI7-AVcFcRm9NzdpkuVQfEFhFs4-tNNEOkwfNu1i_r0dK7i6Z_Gdc-Fj7B7hCQH0c0SwynAQkoOWFrm6YCtUmrjRVl3OGbTgRFpes5sYDzCXUkMr9rhtk7xu6jHJTvujj0kXks00dm3XdFNMPk9x9E28ZVehOEZ_93fXbPf6ssveeb59-8g2Oe-1UBxJ20BKmlIUla-o1ESlSvclCmOpEKHSAqhK0RcVShGMJGFFkJjKAGCQ1uxhme2H7nvycXSHbhra-aMjlJKUVfpM0ULFfqjbLz_8UwjurMMtOtysw_3qcIp-AC6jUAI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3144359571</pqid></control><display><type>article</type><title>On Limit Cycles of Autonomous Systems</title><source>SpringerLink Journals - AutoHoldings</source><creator>Ivanova, T. M. ; Kostin, A. B. ; Rubinshtein, A. I. ; Sherstyukov, V. B.</creator><creatorcontrib>Ivanova, T. M. ; Kostin, A. B. ; Rubinshtein, A. I. ; Sherstyukov, V. B.</creatorcontrib><description>We consider the problem of the existence of limit cycles for autonomous systems of differential equations. We present quite elementary considerations that can be useful in discussing qualitative issues that arise in the course of ordinary differential equations. We establish that any simple closed curve defined by the equation
F
(
x
,
y
) = 1 with a sufficiently general function
F
is a limit cycle for the corresponding autonomous system on the plane (and even for an infinite number of systems depending on the real parameter). These systems are written out explicitly. We analyze in detail several specific examples. Graphic illustrations are provided.</description><identifier>ISSN: 1072-3374</identifier><identifier>EISSN: 1573-8795</identifier><identifier>DOI: 10.1007/s10958-024-07491-5</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Differential equations ; Mathematics ; Mathematics and Statistics ; Qualitative analysis</subject><ispartof>Journal of mathematical sciences (New York, N.Y.), 2024, Vol.286 (1), p.68-88</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024 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><rights>Copyright Springer Nature B.V. 2024</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10958-024-07491-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10958-024-07491-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Ivanova, T. M.</creatorcontrib><creatorcontrib>Kostin, A. B.</creatorcontrib><creatorcontrib>Rubinshtein, A. I.</creatorcontrib><creatorcontrib>Sherstyukov, V. B.</creatorcontrib><title>On Limit Cycles of Autonomous Systems</title><title>Journal of mathematical sciences (New York, N.Y.)</title><addtitle>J Math Sci</addtitle><description>We consider the problem of the existence of limit cycles for autonomous systems of differential equations. We present quite elementary considerations that can be useful in discussing qualitative issues that arise in the course of ordinary differential equations. We establish that any simple closed curve defined by the equation
F
(
x
,
y
) = 1 with a sufficiently general function
F
is a limit cycle for the corresponding autonomous system on the plane (and even for an infinite number of systems depending on the real parameter). These systems are written out explicitly. We analyze in detail several specific examples. Graphic illustrations are provided.</description><subject>Differential equations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Qualitative analysis</subject><issn>1072-3374</issn><issn>1573-8795</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkEtLxDAUhYMoOI7-AVcFcRm9NzdpkuVQfEFhFs4-tNNEOkwfNu1i_r0dK7i6Z_Gdc-Fj7B7hCQH0c0SwynAQkoOWFrm6YCtUmrjRVl3OGbTgRFpes5sYDzCXUkMr9rhtk7xu6jHJTvujj0kXks00dm3XdFNMPk9x9E28ZVehOEZ_93fXbPf6ssveeb59-8g2Oe-1UBxJ20BKmlIUla-o1ESlSvclCmOpEKHSAqhK0RcVShGMJGFFkJjKAGCQ1uxhme2H7nvycXSHbhra-aMjlJKUVfpM0ULFfqjbLz_8UwjurMMtOtysw_3qcIp-AC6jUAI</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Ivanova, T. M.</creator><creator>Kostin, A. B.</creator><creator>Rubinshtein, A. I.</creator><creator>Sherstyukov, V. B.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>2024</creationdate><title>On Limit Cycles of Autonomous Systems</title><author>Ivanova, T. M. ; Kostin, A. B. ; Rubinshtein, A. I. ; Sherstyukov, V. B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p725-1379f3548b2aded3b733b56cb12893a2fd7203d61ead142f843292f4164f00813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Differential equations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Qualitative analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ivanova, T. M.</creatorcontrib><creatorcontrib>Kostin, A. B.</creatorcontrib><creatorcontrib>Rubinshtein, A. I.</creatorcontrib><creatorcontrib>Sherstyukov, V. B.</creatorcontrib><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ivanova, T. M.</au><au>Kostin, A. B.</au><au>Rubinshtein, A. I.</au><au>Sherstyukov, V. B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Limit Cycles of Autonomous Systems</atitle><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle><stitle>J Math Sci</stitle><date>2024</date><risdate>2024</risdate><volume>286</volume><issue>1</issue><spage>68</spage><epage>88</epage><pages>68-88</pages><issn>1072-3374</issn><eissn>1573-8795</eissn><abstract>We consider the problem of the existence of limit cycles for autonomous systems of differential equations. We present quite elementary considerations that can be useful in discussing qualitative issues that arise in the course of ordinary differential equations. We establish that any simple closed curve defined by the equation
F
(
x
,
y
) = 1 with a sufficiently general function
F
is a limit cycle for the corresponding autonomous system on the plane (and even for an infinite number of systems depending on the real parameter). These systems are written out explicitly. We analyze in detail several specific examples. Graphic illustrations are provided.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10958-024-07491-5</doi><tpages>21</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1072-3374 |
| ispartof | Journal of mathematical sciences (New York, N.Y.), 2024, Vol.286 (1), p.68-88 |
| issn | 1072-3374 1573-8795 |
| language | eng |
| recordid | cdi_proquest_journals_3144359571 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Differential equations Mathematics Mathematics and Statistics Qualitative analysis |
| title | On Limit Cycles of Autonomous Systems |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T21%3A36%3A46IST&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=On%20Limit%20Cycles%20of%20Autonomous%20Systems&rft.jtitle=Journal%20of%20mathematical%20sciences%20(New%20York,%20N.Y.)&rft.au=Ivanova,%20T.%20M.&rft.date=2024&rft.volume=286&rft.issue=1&rft.spage=68&rft.epage=88&rft.pages=68-88&rft.issn=1072-3374&rft.eissn=1573-8795&rft_id=info:doi/10.1007/s10958-024-07491-5&rft_dat=%3Cproquest_sprin%3E3144359571%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=3144359571&rft_id=info:pmid/&rfr_iscdi=true |