Existence of Front–Back-Pulse Solutions of a Three-Species Lotka–Volterra Competition–Diffusion System
The existence of nonmonotone traveling wave solutions of the three-species Lotka–Volterra competition diffusion system under strong competition is established. A traveling wave solution can be considered as a heteroclinic orbit of a vector field in R 6 . Under suitable assumptions on parameters of t...
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| Veröffentlicht in: | Journal of dynamics and differential equations 2023-06, Vol.35 (2), p.1273-1308 |
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| container_title | Journal of dynamics and differential equations |
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| creator | Chang, Chueh-Hsin Chen, Chiun-Chuan |
| description | The existence of nonmonotone traveling wave solutions of the three-species Lotka–Volterra competition diffusion system under strong competition is established. A traveling wave solution can be considered as a heteroclinic orbit of a vector field in
R
6
. Under suitable assumptions on parameters of the equations, we apply a bifurcation theory of heteroclinic orbits to show that a three-species traveling wave can bifurcate from two two-species waves which connect to a common equilibrium. The three components of the three-species wave obtained are positive and have the profiles that one is a front, one is a back, and the third component is a pulse between the previous two with a long middle part close to a constant. As applications of our result, we find several explicit regions of parameters of the equations where the bifurcation of three-species traveling waves occur. |
| doi_str_mv | 10.1007/s10884-021-10090-6 |
| format | Article |
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R
6
. Under suitable assumptions on parameters of the equations, we apply a bifurcation theory of heteroclinic orbits to show that a three-species traveling wave can bifurcate from two two-species waves which connect to a common equilibrium. The three components of the three-species wave obtained are positive and have the profiles that one is a front, one is a back, and the third component is a pulse between the previous two with a long middle part close to a constant. As applications of our result, we find several explicit regions of parameters of the equations where the bifurcation of three-species traveling waves occur.</description><identifier>ISSN: 1040-7294</identifier><identifier>EISSN: 1572-9222</identifier><identifier>DOI: 10.1007/s10884-021-10090-6</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Applications of Mathematics ; Bifurcation theory ; Competition ; Fields (mathematics) ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Parameters ; Partial Differential Equations ; Species diffusion ; Traveling waves</subject><ispartof>Journal of dynamics and differential equations, 2023-06, Vol.35 (2), p.1273-1308</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-c5b4585266c3c942822ab0cb02d038d199906f5d18d10c16f9edb0af3e44bbc13</citedby><cites>FETCH-LOGICAL-c319t-c5b4585266c3c942822ab0cb02d038d199906f5d18d10c16f9edb0af3e44bbc13</cites><orcidid>0000-0002-0613-4400</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10884-021-10090-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10884-021-10090-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Chang, Chueh-Hsin</creatorcontrib><creatorcontrib>Chen, Chiun-Chuan</creatorcontrib><title>Existence of Front–Back-Pulse Solutions of a Three-Species Lotka–Volterra Competition–Diffusion System</title><title>Journal of dynamics and differential equations</title><addtitle>J Dyn Diff Equat</addtitle><description>The existence of nonmonotone traveling wave solutions of the three-species Lotka–Volterra competition diffusion system under strong competition is established. A traveling wave solution can be considered as a heteroclinic orbit of a vector field in
R
6
. Under suitable assumptions on parameters of the equations, we apply a bifurcation theory of heteroclinic orbits to show that a three-species traveling wave can bifurcate from two two-species waves which connect to a common equilibrium. The three components of the three-species wave obtained are positive and have the profiles that one is a front, one is a back, and the third component is a pulse between the previous two with a long middle part close to a constant. As applications of our result, we find several explicit regions of parameters of the equations where the bifurcation of three-species traveling waves occur.</description><subject>Applications of Mathematics</subject><subject>Bifurcation theory</subject><subject>Competition</subject><subject>Fields (mathematics)</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Parameters</subject><subject>Partial Differential Equations</subject><subject>Species diffusion</subject><subject>Traveling waves</subject><issn>1040-7294</issn><issn>1572-9222</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KxDAUhYMoOI6-gKuC6-hNmrbJUkdHhQGFGd2GNE2189PUJAVn5zv4hj6JGSu4c3XPTb5zLhyETgmcE4DiwhPgnGGgBMddAM730IhkBcWCUrofNTDABRXsEB15v4QI8VSM0PrmvfHBtNoktk6mzrbh6-PzSukVfuzX3iRzu-5DY1u_-1fJ4tUZg-ed0Y3xycyGlYr8s10H45xKJnbTmdDsDPH5uqnr3kedzLfxyOYYHdQqhp78zjF6mt4sJnd49nB7P7mcYZ0SEbDOSpbxjOa5TrVglFOqStAl0ApSXhEhBOR1VpGoQZO8FqYqQdWpYawsNUnH6GzI7Zx9640Pcml718aTknIiGMkILyJFB0o7670ztexcs1FuKwnIXatyaFXGVuVPqzKPpnQw-Qi3L8b9Rf_j-gZ25H4U</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Chang, Chueh-Hsin</creator><creator>Chen, Chiun-Chuan</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-0613-4400</orcidid></search><sort><creationdate>20230601</creationdate><title>Existence of Front–Back-Pulse Solutions of a Three-Species Lotka–Volterra Competition–Diffusion System</title><author>Chang, Chueh-Hsin ; Chen, Chiun-Chuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-c5b4585266c3c942822ab0cb02d038d199906f5d18d10c16f9edb0af3e44bbc13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Applications of Mathematics</topic><topic>Bifurcation theory</topic><topic>Competition</topic><topic>Fields (mathematics)</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><topic>Parameters</topic><topic>Partial Differential Equations</topic><topic>Species diffusion</topic><topic>Traveling waves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chang, Chueh-Hsin</creatorcontrib><creatorcontrib>Chen, Chiun-Chuan</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of dynamics and differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chang, Chueh-Hsin</au><au>Chen, Chiun-Chuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence of Front–Back-Pulse Solutions of a Three-Species Lotka–Volterra Competition–Diffusion System</atitle><jtitle>Journal of dynamics and differential equations</jtitle><stitle>J Dyn Diff Equat</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>35</volume><issue>2</issue><spage>1273</spage><epage>1308</epage><pages>1273-1308</pages><issn>1040-7294</issn><eissn>1572-9222</eissn><abstract>The existence of nonmonotone traveling wave solutions of the three-species Lotka–Volterra competition diffusion system under strong competition is established. A traveling wave solution can be considered as a heteroclinic orbit of a vector field in
R
6
. Under suitable assumptions on parameters of the equations, we apply a bifurcation theory of heteroclinic orbits to show that a three-species traveling wave can bifurcate from two two-species waves which connect to a common equilibrium. The three components of the three-species wave obtained are positive and have the profiles that one is a front, one is a back, and the third component is a pulse between the previous two with a long middle part close to a constant. As applications of our result, we find several explicit regions of parameters of the equations where the bifurcation of three-species traveling waves occur.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10884-021-10090-6</doi><tpages>36</tpages><orcidid>https://orcid.org/0000-0002-0613-4400</orcidid></addata></record> |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Applications of Mathematics Bifurcation theory Competition Fields (mathematics) Mathematical analysis Mathematics Mathematics and Statistics Ordinary Differential Equations Parameters Partial Differential Equations Species diffusion Traveling waves |
| title | Existence of Front–Back-Pulse Solutions of a Three-Species Lotka–Volterra Competition–Diffusion System |
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