The effect of the defensive strategy taken by the prey on predator–prey interaction
In this paper, we scrutinize a delayed predator-model for the purpose of studying the impact of the strategy considered by the prey population on the evolution of the studied species. The main presumption is to consider the existence of two prey types with different behaviors. The first, has a socia...
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| Veröffentlicht in: | Journal of applied mathematics & computing 2020-10, Vol.64 (1-2), p.665-690 |
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| container_title | Journal of applied mathematics & computing |
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| creator | Souna, Fethi Lakmeche, Abdelkader Djilali, Salih |
| description | In this paper, we scrutinize a delayed predator-model for the purpose of studying the impact of the strategy considered by the prey population on the evolution of the studied species. The main presumption is to consider the existence of two prey types with different behaviors. The first, has a social behavior and takes the advantage of living in group for the purpose of defending each others, and the second one has a solitary behavior. A mathematical approach is used to study this effect, where the local stability and bifurcation analysis are examined. Indeed, we establish that the system under consideration has a rich dynamics such as Hopf bifurcation in both the absence and the presence of time lags. Further the stability of the periodic solution generated by the presence of the time lags are discussed using the normal form. Some numerical simulations are provided for ensuring the obtained mathematical results. |
| doi_str_mv | 10.1007/s12190-020-01373-0 |
| format | Article |
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Some numerical simulations are provided for ensuring the obtained mathematical results.</description><subject>Applied mathematics</subject><subject>Canonical forms</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Computer simulation</subject><subject>Hopf bifurcation</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Original Research</subject><subject>Predator-prey simulation</subject><subject>Stability analysis</subject><subject>Theory of Computation</subject><issn>1598-5865</issn><issn>1865-2085</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9UMtOwzAQtBBIlMIPcIrE2bC2Yyc-ogooUiUu7dlyknVJgaTYLlJu_AN_yJfgNkjcOKz2NTOrHUIuGVwzgOImMM40UOApmCgEhSMyYaWSlEMpj1MtdUllGpySsxA2AKrQoCdktXzGDJ3DOma9y2LqGnTYhfYDsxC9jbgesmhfsMuq4bDfehyyvtvnxsbef39-HUZtF9HbOrZ9d05OnH0NePGbp2R1f7eczeni6eFxdrugtWA60rKARiLoUqlaCVG7SjWgrELkHETTOJQ1MpXzSrlcuPSXFgwqJYXj2koupuRq1N36_n2HIZpNv_NdOml4nnPBlBZ7FB9Rte9D8OjM1rdv1g-GgdnbZ0b7TLLPHOwzkEhiJIUE7tbo_6T_Yf0AeBpzUQ</recordid><startdate>20201001</startdate><enddate>20201001</enddate><creator>Souna, Fethi</creator><creator>Lakmeche, Abdelkader</creator><creator>Djilali, Salih</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><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><orcidid>https://orcid.org/0000-0002-4030-6499</orcidid></search><sort><creationdate>20201001</creationdate><title>The effect of the defensive strategy taken by the prey on predator–prey interaction</title><author>Souna, Fethi ; Lakmeche, Abdelkader ; Djilali, Salih</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-870d5e09866c633cfb6d06a6ee2203ddfe5ce1642b6f43f3739310b653f29a523</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Applied mathematics</topic><topic>Canonical forms</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Computer simulation</topic><topic>Hopf bifurcation</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Original Research</topic><topic>Predator-prey simulation</topic><topic>Stability analysis</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Souna, Fethi</creatorcontrib><creatorcontrib>Lakmeche, Abdelkader</creatorcontrib><creatorcontrib>Djilali, Salih</creatorcontrib><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>Journal of applied mathematics & computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Souna, Fethi</au><au>Lakmeche, Abdelkader</au><au>Djilali, Salih</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The effect of the defensive strategy taken by the prey on predator–prey interaction</atitle><jtitle>Journal of applied mathematics & computing</jtitle><stitle>J. 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| subjects | Applied mathematics Canonical forms Computational Mathematics and Numerical Analysis Computer simulation Hopf bifurcation Mathematical analysis Mathematical and Computational Engineering Mathematical models Mathematics Mathematics and Statistics Mathematics of Computing Original Research Predator-prey simulation Stability analysis Theory of Computation |
| title | The effect of the defensive strategy taken by the prey on predator–prey interaction |
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