Global dynamics and traveling wave solutions for a three‐species model
In this work, we investigate the system of a three‐species ecological model involving one predator–prey subsystem coupling with a generalist predator with negative effect on the prey. Without diffusive terms, all global dynamics of its corresponding reaction equations are proved analytically for all...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2022-03, Vol.45 (4), p.2380-2397 |
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| creator | Li, Fanfan Han, Zhenlai Yang, Ting‐Hui |
| description | In this work, we investigate the system of a three‐species ecological model involving one predator–prey subsystem coupling with a generalist predator with negative effect on the prey. Without diffusive terms, all global dynamics of its corresponding reaction equations are proved analytically for all classified parameters. With diffusive terms, the transitions of different spatial homogeneous solutions, the existence of traveling wave solutions, are investigated by a higher dimensional shooting method, the Wazewski method. These mathematical results, under mild conditions, imply that a generalist predator can stabilize a predator–prey system even with negative effects of coupling. Finally, some biological implications are given and the interesting numerical simulations are performed. |
| doi_str_mv | 10.1002/mma.7934 |
| format | Article |
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Without diffusive terms, all global dynamics of its corresponding reaction equations are proved analytically for all classified parameters. With diffusive terms, the transitions of different spatial homogeneous solutions, the existence of traveling wave solutions, are investigated by a higher dimensional shooting method, the Wazewski method. These mathematical results, under mild conditions, imply that a generalist predator can stabilize a predator–prey system even with negative effects of coupling. Finally, some biological implications are given and the interesting numerical simulations are performed.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.7934</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>Coupling ; Ecological models ; global asymptotically stability ; Mathematical models ; Predator-prey simulation ; Predators ; Subsystems ; traveling wave solutions ; Traveling waves ; two predators–one prey system ; Wazewski principle</subject><ispartof>Mathematical methods in the applied sciences, 2022-03, Vol.45 (4), p.2380-2397</ispartof><rights>2021 John Wiley & Sons, Ltd.</rights><rights>2022 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c1844-22579ac3f9e75767dde291ae84a72598dbb0a0b24065f4b06f311887b74699eb3</cites><orcidid>0000-0003-2079-2597</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fmma.7934$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.7934$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Li, Fanfan</creatorcontrib><creatorcontrib>Han, Zhenlai</creatorcontrib><creatorcontrib>Yang, Ting‐Hui</creatorcontrib><title>Global dynamics and traveling wave solutions for a three‐species model</title><title>Mathematical methods in the applied sciences</title><description>In this work, we investigate the system of a three‐species ecological model involving one predator–prey subsystem coupling with a generalist predator with negative effect on the prey. 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Finally, some biological implications are given and the interesting numerical simulations are performed.</description><subject>Coupling</subject><subject>Ecological models</subject><subject>global asymptotically stability</subject><subject>Mathematical models</subject><subject>Predator-prey simulation</subject><subject>Predators</subject><subject>Subsystems</subject><subject>traveling wave solutions</subject><subject>Traveling waves</subject><subject>two predators–one prey system</subject><subject>Wazewski principle</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp10LFOwzAQgGELgUQpSDyCJRaWlLPj2PFYVdAitWKB2bKTC6RK4mKnVN14BJ6RJyGlrEx3w6c76SfkmsGEAfC7trUTpVNxQkYMtE6YUPKUjIApSARn4pxcxLgGgJwxPiKLeeOdbWi572xbF5HarqR9sB_Y1N0r3Q0Ljb7Z9rXvIq18oJb2bwHx-_MrbrCoMdLWl9hckrPKNhGv_uaYvDzcP88WyfJp_jibLpOC5UIknGdK2yKtNKpMSVWWyDWzmAureKbz0jmw4LgAmVXCgaxSxvJcOSWk1ujSMbk53t0E_77F2Ju134ZueGm45BK0lCwb1O1RFcHHGLAym1C3NuwNA3PoZIZO5tBpoMmR7uoG9_86s1pNf_0Pd-BpGQ</recordid><startdate>20220315</startdate><enddate>20220315</enddate><creator>Li, Fanfan</creator><creator>Han, Zhenlai</creator><creator>Yang, Ting‐Hui</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0003-2079-2597</orcidid></search><sort><creationdate>20220315</creationdate><title>Global dynamics and traveling wave solutions for a three‐species model</title><author>Li, Fanfan ; Han, Zhenlai ; Yang, Ting‐Hui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1844-22579ac3f9e75767dde291ae84a72598dbb0a0b24065f4b06f311887b74699eb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Coupling</topic><topic>Ecological models</topic><topic>global asymptotically stability</topic><topic>Mathematical models</topic><topic>Predator-prey simulation</topic><topic>Predators</topic><topic>Subsystems</topic><topic>traveling wave solutions</topic><topic>Traveling waves</topic><topic>two predators–one prey system</topic><topic>Wazewski principle</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Fanfan</creatorcontrib><creatorcontrib>Han, Zhenlai</creatorcontrib><creatorcontrib>Yang, Ting‐Hui</creatorcontrib><collection>CrossRef</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><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Fanfan</au><au>Han, Zhenlai</au><au>Yang, Ting‐Hui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Global dynamics and traveling wave solutions for a three‐species model</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2022-03-15</date><risdate>2022</risdate><volume>45</volume><issue>4</issue><spage>2380</spage><epage>2397</epage><pages>2380-2397</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>In this work, we investigate the system of a three‐species ecological model involving one predator–prey subsystem coupling with a generalist predator with negative effect on the prey. 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| subjects | Coupling Ecological models global asymptotically stability Mathematical models Predator-prey simulation Predators Subsystems traveling wave solutions Traveling waves two predators–one prey system Wazewski principle |
| title | Global dynamics and traveling wave solutions for a three‐species model |
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