HOPF BIFURCATION ANALYSIS FOR A RATIO-DEPENDENT PREDATOR–PREY SYSTEM INVOLVING TWO DELAYS
The aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator–prey system involving two discrete delays. A delay parameter is chosen as the bifurcation parameter for the analysis. Stability of the bifurcating periodic solutions is determined by using the cent...
Gespeichert in:
| Veröffentlicht in: | The ANZIAM journal 2014-01, Vol.55 (3), p.214-231 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 231 |
|---|---|
| container_issue | 3 |
| container_start_page | 214 |
| container_title | The ANZIAM journal |
| container_volume | 55 |
| creator | KARAOGLU, E. MERDAN, H. |
| description | The aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator–prey system involving two discrete delays. A delay parameter is chosen as the bifurcation parameter for the analysis. Stability of the bifurcating periodic solutions is determined by using the centre manifold theorem and the normal form theory introduced by Hassard et al. Some of the bifurcation properties including the direction, stability and period are given. Finally, our theoretical results are supported by some numerical simulations. |
| doi_str_mv | 10.1017/S1446181114000054 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1660044513</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_S1446181114000054</cupid><sourcerecordid>1660044513</sourcerecordid><originalsourceid>FETCH-LOGICAL-c398t-af717fd905847f78748bdbef1b07ed26b061a9ad93c25c5362492894e6f23f363</originalsourceid><addsrcrecordid>eNp9UM1Og0AY3BhNrNUH8LZHL-guu-zCEQu0JMg2QGuIB8LPrmnTlsq2B2--g2_okwhpbyZ-l28y38yXzABwj9EjRpg_pZhShm2MMUX9WPQCjAbKsDmxLs94uF-DG63XCFHCiTkCbzMxD-BzGCySiZuFIoZu7EZ5GqYwEAl0YTKwhufP_djz4wzOE99zM5H8fH33MIdpnmb-CwzjpYiWYTyF2auAnh-5eXoLrlS50fLuvMdgEfjZZGZEYhpO3MioiWMfjFJxzFXjIMumXHGbU7tqKqlwhbhsTFYhhkunbBxSm1ZtEWZSx7QdKpkyiSKMjMHD6e--az-OUh-K7UrXcrMpd7I96gIz1uelFia9FJ-kdddq3UlV7LvVtuw-C4yKocjiT5G9h5w95bbqVs27LNbtsdv1kf5x_QJIZm1H</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1660044513</pqid></control><display><type>article</type><title>HOPF BIFURCATION ANALYSIS FOR A RATIO-DEPENDENT PREDATOR–PREY SYSTEM INVOLVING TWO DELAYS</title><source>Alma/SFX Local Collection</source><creator>KARAOGLU, E. ; MERDAN, H.</creator><creatorcontrib>KARAOGLU, E. ; MERDAN, H.</creatorcontrib><description>The aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator–prey system involving two discrete delays. A delay parameter is chosen as the bifurcation parameter for the analysis. Stability of the bifurcating periodic solutions is determined by using the centre manifold theorem and the normal form theory introduced by Hassard et al. Some of the bifurcation properties including the direction, stability and period are given. Finally, our theoretical results are supported by some numerical simulations.</description><identifier>ISSN: 1446-1811</identifier><identifier>EISSN: 1446-8735</identifier><identifier>DOI: 10.1017/S1446181114000054</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Bifurcation theory ; Bifurcations ; Computer simulation ; Delay ; Hopf bifurcation ; Manifolds ; Mathematical models ; Stability</subject><ispartof>The ANZIAM journal, 2014-01, Vol.55 (3), p.214-231</ispartof><rights>Copyright © 2014 Australian Mathematical Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c398t-af717fd905847f78748bdbef1b07ed26b061a9ad93c25c5362492894e6f23f363</citedby><cites>FETCH-LOGICAL-c398t-af717fd905847f78748bdbef1b07ed26b061a9ad93c25c5362492894e6f23f363</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>KARAOGLU, E.</creatorcontrib><creatorcontrib>MERDAN, H.</creatorcontrib><title>HOPF BIFURCATION ANALYSIS FOR A RATIO-DEPENDENT PREDATOR–PREY SYSTEM INVOLVING TWO DELAYS</title><title>The ANZIAM journal</title><addtitle>ANZIAM J</addtitle><description>The aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator–prey system involving two discrete delays. A delay parameter is chosen as the bifurcation parameter for the analysis. Stability of the bifurcating periodic solutions is determined by using the centre manifold theorem and the normal form theory introduced by Hassard et al. Some of the bifurcation properties including the direction, stability and period are given. Finally, our theoretical results are supported by some numerical simulations.</description><subject>Bifurcation theory</subject><subject>Bifurcations</subject><subject>Computer simulation</subject><subject>Delay</subject><subject>Hopf bifurcation</subject><subject>Manifolds</subject><subject>Mathematical models</subject><subject>Stability</subject><issn>1446-1811</issn><issn>1446-8735</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9UM1Og0AY3BhNrNUH8LZHL-guu-zCEQu0JMg2QGuIB8LPrmnTlsq2B2--g2_okwhpbyZ-l28y38yXzABwj9EjRpg_pZhShm2MMUX9WPQCjAbKsDmxLs94uF-DG63XCFHCiTkCbzMxD-BzGCySiZuFIoZu7EZ5GqYwEAl0YTKwhufP_djz4wzOE99zM5H8fH33MIdpnmb-CwzjpYiWYTyF2auAnh-5eXoLrlS50fLuvMdgEfjZZGZEYhpO3MioiWMfjFJxzFXjIMumXHGbU7tqKqlwhbhsTFYhhkunbBxSm1ZtEWZSx7QdKpkyiSKMjMHD6e--az-OUh-K7UrXcrMpd7I96gIz1uelFia9FJ-kdddq3UlV7LvVtuw-C4yKocjiT5G9h5w95bbqVs27LNbtsdv1kf5x_QJIZm1H</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>KARAOGLU, E.</creator><creator>MERDAN, H.</creator><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>20140101</creationdate><title>HOPF BIFURCATION ANALYSIS FOR A RATIO-DEPENDENT PREDATOR–PREY SYSTEM INVOLVING TWO DELAYS</title><author>KARAOGLU, E. ; MERDAN, H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c398t-af717fd905847f78748bdbef1b07ed26b061a9ad93c25c5362492894e6f23f363</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Bifurcation theory</topic><topic>Bifurcations</topic><topic>Computer simulation</topic><topic>Delay</topic><topic>Hopf bifurcation</topic><topic>Manifolds</topic><topic>Mathematical models</topic><topic>Stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>KARAOGLU, E.</creatorcontrib><creatorcontrib>MERDAN, H.</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>The ANZIAM journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>KARAOGLU, E.</au><au>MERDAN, H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>HOPF BIFURCATION ANALYSIS FOR A RATIO-DEPENDENT PREDATOR–PREY SYSTEM INVOLVING TWO DELAYS</atitle><jtitle>The ANZIAM journal</jtitle><addtitle>ANZIAM J</addtitle><date>2014-01-01</date><risdate>2014</risdate><volume>55</volume><issue>3</issue><spage>214</spage><epage>231</epage><pages>214-231</pages><issn>1446-1811</issn><eissn>1446-8735</eissn><abstract>The aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator–prey system involving two discrete delays. A delay parameter is chosen as the bifurcation parameter for the analysis. Stability of the bifurcating periodic solutions is determined by using the centre manifold theorem and the normal form theory introduced by Hassard et al. Some of the bifurcation properties including the direction, stability and period are given. Finally, our theoretical results are supported by some numerical simulations.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S1446181114000054</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1446-1811 |
| ispartof | The ANZIAM journal, 2014-01, Vol.55 (3), p.214-231 |
| issn | 1446-1811 1446-8735 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1660044513 |
| source | Alma/SFX Local Collection |
| subjects | Bifurcation theory Bifurcations Computer simulation Delay Hopf bifurcation Manifolds Mathematical models Stability |
| title | HOPF BIFURCATION ANALYSIS FOR A RATIO-DEPENDENT PREDATOR–PREY SYSTEM INVOLVING TWO DELAYS |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T21%3A05%3A02IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=HOPF%20BIFURCATION%20ANALYSIS%20FOR%20A%20RATIO-DEPENDENT%20PREDATOR%E2%80%93PREY%20SYSTEM%20INVOLVING%20TWO%20DELAYS&rft.jtitle=The%20ANZIAM%20journal&rft.au=KARAOGLU,%20E.&rft.date=2014-01-01&rft.volume=55&rft.issue=3&rft.spage=214&rft.epage=231&rft.pages=214-231&rft.issn=1446-1811&rft.eissn=1446-8735&rft_id=info:doi/10.1017/S1446181114000054&rft_dat=%3Cproquest_cross%3E1660044513%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1660044513&rft_id=info:pmid/&rft_cupid=10_1017_S1446181114000054&rfr_iscdi=true |