Modelling and analysis of a competitive model with stage structure
A two-species Lotka-Volterra type competition model with stage structures for both species is proposed and investigated. In our model, the individuals of each species are classified as belonging either the immature or the mature. First, we consider the stage-structured model with constant coefficien...
Gespeichert in:
| Veröffentlicht in: | Mathematical and computer modelling 2005, Vol.41 (2), p.159-175 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 175 |
|---|---|
| container_issue | 2 |
| container_start_page | 159 |
| container_title | Mathematical and computer modelling |
| container_volume | 41 |
| creator | Xu, Rui Chaplain, M.A.J. Davidson, F.A. |
| description | A two-species Lotka-Volterra type competition model with stage structures for both species is proposed and investigated. In our model, the individuals of each species are classified as belonging either the immature or the mature. First, we consider the stage-structured model with constant coefficients. By constructing suitable Lyapunov functions, sufficient conditions are derived for the global stability of nonnegative equilibria of the proposed model. It is shown that three typical dynamical behaviors (coexistence, bistability, dominance) are possible in stage-structured competition model. Next, we consider the stage-structured competitive model in which the coefficients are assumed to be positively continuous periodic functions. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are obtained for the existence of positive periodic solutions to the model. Numerical simulations are also presented to illustrate the feasibility of our main results. |
| doi_str_mv | 10.1016/j.mcm.2004.08.003 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_29363114</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0895717705000725</els_id><sourcerecordid>29363114</sourcerecordid><originalsourceid>FETCH-LOGICAL-c401t-1a0825a26c015c7ca4c5043e51515bf480835c42b2e93b98e8010afc347f19393</originalsourceid><addsrcrecordid>eNp9kMtOwzAQRS0EEqXwAeyygV3COHYSW6yg4iUVsYG15U4nxVUexU6K-ve4KhI7NJqZzbnzuIxdcsg48PJmnbXYZjmAzEBlAOKITbiq8lTLSh-zCShdpBWvqlN2FsIaAAoNasLuX_slNY3rVontljFtswsuJH2d2AT7dkODG9yWknbPJd9u-EzCYFcUqx9xGD2ds5PaNoEufvuUfTw-vM-e0_nb08vsbp6iBD6k3ILKC5uXCLzACq3EAqSggsdY1FKBEgXKfJGTFgutSAEHW6OQVc210GLKrg9zN77_GikMpnUB4_G2o34MJteiFJzLCPIDiL4PwVNtNt611u8MB7N3y6xNdMvs3TKgTHQraq5-h9uAtqm97dCFP2FZ6Lwsy8jdHjiKn24deRPQUYe0dJ5wMMve_bPlB6i7fjY</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>29363114</pqid></control><display><type>article</type><title>Modelling and analysis of a competitive model with stage structure</title><source>Elsevier ScienceDirect Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Xu, Rui ; Chaplain, M.A.J. ; Davidson, F.A.</creator><creatorcontrib>Xu, Rui ; Chaplain, M.A.J. ; Davidson, F.A.</creatorcontrib><description>A two-species Lotka-Volterra type competition model with stage structures for both species is proposed and investigated. In our model, the individuals of each species are classified as belonging either the immature or the mature. First, we consider the stage-structured model with constant coefficients. By constructing suitable Lyapunov functions, sufficient conditions are derived for the global stability of nonnegative equilibria of the proposed model. It is shown that three typical dynamical behaviors (coexistence, bistability, dominance) are possible in stage-structured competition model. Next, we consider the stage-structured competitive model in which the coefficients are assumed to be positively continuous periodic functions. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are obtained for the existence of positive periodic solutions to the model. Numerical simulations are also presented to illustrate the feasibility of our main results.</description><identifier>ISSN: 0895-7177</identifier><identifier>EISSN: 1872-9479</identifier><identifier>DOI: 10.1016/j.mcm.2004.08.003</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Competition ; Exact sciences and technology ; Global analysis, analysis on manifolds ; Global stability ; Mathematical analysis ; Mathematics ; Ordinary differential equations ; Periodic solution ; Sciences and techniques of general use ; Stage structure ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Mathematical and computer modelling, 2005, Vol.41 (2), p.159-175</ispartof><rights>2005 Elsevier Ltd. All rights reserved</rights><rights>2005 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c401t-1a0825a26c015c7ca4c5043e51515bf480835c42b2e93b98e8010afc347f19393</citedby><cites>FETCH-LOGICAL-c401t-1a0825a26c015c7ca4c5043e51515bf480835c42b2e93b98e8010afc347f19393</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0895717705000725$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,4010,27900,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16592666$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Xu, Rui</creatorcontrib><creatorcontrib>Chaplain, M.A.J.</creatorcontrib><creatorcontrib>Davidson, F.A.</creatorcontrib><title>Modelling and analysis of a competitive model with stage structure</title><title>Mathematical and computer modelling</title><description>A two-species Lotka-Volterra type competition model with stage structures for both species is proposed and investigated. In our model, the individuals of each species are classified as belonging either the immature or the mature. First, we consider the stage-structured model with constant coefficients. By constructing suitable Lyapunov functions, sufficient conditions are derived for the global stability of nonnegative equilibria of the proposed model. It is shown that three typical dynamical behaviors (coexistence, bistability, dominance) are possible in stage-structured competition model. Next, we consider the stage-structured competitive model in which the coefficients are assumed to be positively continuous periodic functions. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are obtained for the existence of positive periodic solutions to the model. Numerical simulations are also presented to illustrate the feasibility of our main results.</description><subject>Competition</subject><subject>Exact sciences and technology</subject><subject>Global analysis, analysis on manifolds</subject><subject>Global stability</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Ordinary differential equations</subject><subject>Periodic solution</subject><subject>Sciences and techniques of general use</subject><subject>Stage structure</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>0895-7177</issn><issn>1872-9479</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEqXwAeyygV3COHYSW6yg4iUVsYG15U4nxVUexU6K-ve4KhI7NJqZzbnzuIxdcsg48PJmnbXYZjmAzEBlAOKITbiq8lTLSh-zCShdpBWvqlN2FsIaAAoNasLuX_slNY3rVontljFtswsuJH2d2AT7dkODG9yWknbPJd9u-EzCYFcUqx9xGD2ds5PaNoEufvuUfTw-vM-e0_nb08vsbp6iBD6k3ILKC5uXCLzACq3EAqSggsdY1FKBEgXKfJGTFgutSAEHW6OQVc210GLKrg9zN77_GikMpnUB4_G2o34MJteiFJzLCPIDiL4PwVNtNt611u8MB7N3y6xNdMvs3TKgTHQraq5-h9uAtqm97dCFP2FZ6Lwsy8jdHjiKn24deRPQUYe0dJ5wMMve_bPlB6i7fjY</recordid><startdate>2005</startdate><enddate>2005</enddate><creator>Xu, Rui</creator><creator>Chaplain, M.A.J.</creator><creator>Davidson, F.A.</creator><general>Elsevier Ltd</general><general>Elsevier Science</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><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>2005</creationdate><title>Modelling and analysis of a competitive model with stage structure</title><author>Xu, Rui ; Chaplain, M.A.J. ; Davidson, F.A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c401t-1a0825a26c015c7ca4c5043e51515bf480835c42b2e93b98e8010afc347f19393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Competition</topic><topic>Exact sciences and technology</topic><topic>Global analysis, analysis on manifolds</topic><topic>Global stability</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Ordinary differential equations</topic><topic>Periodic solution</topic><topic>Sciences and techniques of general use</topic><topic>Stage structure</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xu, Rui</creatorcontrib><creatorcontrib>Chaplain, M.A.J.</creatorcontrib><creatorcontrib>Davidson, F.A.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><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>Mathematical and computer modelling</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xu, Rui</au><au>Chaplain, M.A.J.</au><au>Davidson, F.A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Modelling and analysis of a competitive model with stage structure</atitle><jtitle>Mathematical and computer modelling</jtitle><date>2005</date><risdate>2005</risdate><volume>41</volume><issue>2</issue><spage>159</spage><epage>175</epage><pages>159-175</pages><issn>0895-7177</issn><eissn>1872-9479</eissn><abstract>A two-species Lotka-Volterra type competition model with stage structures for both species is proposed and investigated. In our model, the individuals of each species are classified as belonging either the immature or the mature. First, we consider the stage-structured model with constant coefficients. By constructing suitable Lyapunov functions, sufficient conditions are derived for the global stability of nonnegative equilibria of the proposed model. It is shown that three typical dynamical behaviors (coexistence, bistability, dominance) are possible in stage-structured competition model. Next, we consider the stage-structured competitive model in which the coefficients are assumed to be positively continuous periodic functions. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are obtained for the existence of positive periodic solutions to the model. Numerical simulations are also presented to illustrate the feasibility of our main results.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.mcm.2004.08.003</doi><tpages>17</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0895-7177 |
| ispartof | Mathematical and computer modelling, 2005, Vol.41 (2), p.159-175 |
| issn | 0895-7177 1872-9479 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_29363114 |
| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Competition Exact sciences and technology Global analysis, analysis on manifolds Global stability Mathematical analysis Mathematics Ordinary differential equations Periodic solution Sciences and techniques of general use Stage structure Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Modelling and analysis of a competitive model with stage structure |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-28T16%3A24%3A30IST&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=Modelling%20and%20analysis%20of%20a%20competitive%20model%20with%20stage%20structure&rft.jtitle=Mathematical%20and%20computer%20modelling&rft.au=Xu,%20Rui&rft.date=2005&rft.volume=41&rft.issue=2&rft.spage=159&rft.epage=175&rft.pages=159-175&rft.issn=0895-7177&rft.eissn=1872-9479&rft_id=info:doi/10.1016/j.mcm.2004.08.003&rft_dat=%3Cproquest_cross%3E29363114%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=29363114&rft_id=info:pmid/&rft_els_id=S0895717705000725&rfr_iscdi=true |