Dynamics and simulations of a stochastic predator-prey model with infinite delay and impulsive perturbations
This paper considers a stochastic predator-prey model with infinite delay and impulsive perturbations. Sufficient conditions for permanence in time average are established as well as extinction, stability in time average and global attractivity of the stochasic model. Some simulation figures, which...
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| Veröffentlicht in: | Journal of applied mathematics & computing 2018-06, Vol.57 (1-2), p.437-465 |
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| container_title | Journal of applied mathematics & computing |
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| creator | Lu, Chun Chen, Jian Fan, Xingkui Zhang, Lei |
| description | This paper considers a stochastic predator-prey model with infinite delay and impulsive perturbations. Sufficient conditions for permanence in time average are established as well as extinction, stability in time average and global attractivity of the stochasic model. Some simulation figures, which are obtained by the split-step
θ
-method to discretize the stochasic model, are introduced to support the analytical findings. Our results demonstrate that, firstly, impulsive perturbations which may represent human factor play a key role in maintaining ecological balance; secondly, environmental noise, which can be modelled by Brownian motion, is disadvantageous to population survival; finally, infinite delay has not affect permanence in time average, extinction, stability in time average and global attractivity of the stochasic model. |
| doi_str_mv | 10.1007/s12190-017-1114-3 |
| format | Article |
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θ
-method to discretize the stochasic model, are introduced to support the analytical findings. Our results demonstrate that, firstly, impulsive perturbations which may represent human factor play a key role in maintaining ecological balance; secondly, environmental noise, which can be modelled by Brownian motion, is disadvantageous to population survival; finally, infinite delay has not affect permanence in time average, extinction, stability in time average and global attractivity of the stochasic model.</description><identifier>ISSN: 1598-5865</identifier><identifier>EISSN: 1865-2085</identifier><identifier>DOI: 10.1007/s12190-017-1114-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied mathematics ; Background noise ; Brownian motion ; Computational Mathematics and Numerical Analysis ; Computer simulation ; Delay ; Extinction ; Mathematical and Computational Engineering ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Original Research ; Predator-prey simulation ; Stability ; Stochastic models ; Theory of Computation</subject><ispartof>Journal of applied mathematics & computing, 2018-06, Vol.57 (1-2), p.437-465</ispartof><rights>Korean Society for Computational and Applied Mathematics 2017</rights><rights>Journal of Applied Mathematics and Computing is a copyright of Springer, (2017). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-572e81708fcf27fd5f46ce434e8b1cba42f87f05daf6bde09d9e6d7bf4090ea3</citedby><cites>FETCH-LOGICAL-c316t-572e81708fcf27fd5f46ce434e8b1cba42f87f05daf6bde09d9e6d7bf4090ea3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12190-017-1114-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12190-017-1114-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Lu, Chun</creatorcontrib><creatorcontrib>Chen, Jian</creatorcontrib><creatorcontrib>Fan, Xingkui</creatorcontrib><creatorcontrib>Zhang, Lei</creatorcontrib><title>Dynamics and simulations of a stochastic predator-prey model with infinite delay and impulsive perturbations</title><title>Journal of applied mathematics & computing</title><addtitle>J. Appl. Math. Comput</addtitle><description>This paper considers a stochastic predator-prey model with infinite delay and impulsive perturbations. Sufficient conditions for permanence in time average are established as well as extinction, stability in time average and global attractivity of the stochasic model. Some simulation figures, which are obtained by the split-step
θ
-method to discretize the stochasic model, are introduced to support the analytical findings. Our results demonstrate that, firstly, impulsive perturbations which may represent human factor play a key role in maintaining ecological balance; secondly, environmental noise, which can be modelled by Brownian motion, is disadvantageous to population survival; finally, infinite delay has not affect permanence in time average, extinction, stability in time average and global attractivity of the stochasic model.</description><subject>Applied mathematics</subject><subject>Background noise</subject><subject>Brownian motion</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Computer simulation</subject><subject>Delay</subject><subject>Extinction</subject><subject>Mathematical and Computational Engineering</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</subject><subject>Stochastic models</subject><subject>Theory of Computation</subject><issn>1598-5865</issn><issn>1865-2085</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kEtLxDAUhYMoOI7-AHcB19EkfaRZyviEATezD2keToa2qUmq9N-bsYIrV_dwOOdc-AC4JviWYMzuIqGEY4QJQ4SQEhUnYEWaukIUN9Vp1hVvUJWNc3AR4wHjmnHMV6B7mAfZOxWhHDSMrp86mZwfIvQWShiTV3sZk1NwDEbL5APKYoa916aDXy7toRusG1wyMDty_tlx_Th10X0aOJqQptAum5fgzMoumqvfuwa7p8fd5gVt355fN_dbpApSJ1QxahrCcGOVpczqypa1MmVRmqYlqpUltQ2zuNLS1q02mGtuas1aW2KOjSzW4GaZHYP_mExM4uCnMOSPgmLKC16SguYUWVIq-BiDsWIMrpdhFgSLI1OxMBWZqTgyFUXu0KUTc3Z4N-Fv-f_SN4gMfII</recordid><startdate>20180601</startdate><enddate>20180601</enddate><creator>Lu, Chun</creator><creator>Chen, Jian</creator><creator>Fan, Xingkui</creator><creator>Zhang, Lei</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20180601</creationdate><title>Dynamics and simulations of a stochastic predator-prey model with infinite delay and impulsive perturbations</title><author>Lu, Chun ; Chen, Jian ; Fan, Xingkui ; Zhang, Lei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-572e81708fcf27fd5f46ce434e8b1cba42f87f05daf6bde09d9e6d7bf4090ea3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Applied mathematics</topic><topic>Background noise</topic><topic>Brownian motion</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Computer simulation</topic><topic>Delay</topic><topic>Extinction</topic><topic>Mathematical and Computational Engineering</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</topic><topic>Stochastic models</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lu, Chun</creatorcontrib><creatorcontrib>Chen, Jian</creatorcontrib><creatorcontrib>Fan, Xingkui</creatorcontrib><creatorcontrib>Zhang, Lei</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Journal of applied mathematics & computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lu, Chun</au><au>Chen, Jian</au><au>Fan, Xingkui</au><au>Zhang, Lei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamics and simulations of a stochastic predator-prey model with infinite delay and impulsive perturbations</atitle><jtitle>Journal of applied mathematics & computing</jtitle><stitle>J. Appl. Math. Comput</stitle><date>2018-06-01</date><risdate>2018</risdate><volume>57</volume><issue>1-2</issue><spage>437</spage><epage>465</epage><pages>437-465</pages><issn>1598-5865</issn><eissn>1865-2085</eissn><abstract>This paper considers a stochastic predator-prey model with infinite delay and impulsive perturbations. Sufficient conditions for permanence in time average are established as well as extinction, stability in time average and global attractivity of the stochasic model. Some simulation figures, which are obtained by the split-step
θ
-method to discretize the stochasic model, are introduced to support the analytical findings. Our results demonstrate that, firstly, impulsive perturbations which may represent human factor play a key role in maintaining ecological balance; secondly, environmental noise, which can be modelled by Brownian motion, is disadvantageous to population survival; finally, infinite delay has not affect permanence in time average, extinction, stability in time average and global attractivity of the stochasic model.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s12190-017-1114-3</doi><tpages>29</tpages></addata></record> |
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| subjects | Applied mathematics Background noise Brownian motion Computational Mathematics and Numerical Analysis Computer simulation Delay Extinction Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Original Research Predator-prey simulation Stability Stochastic models Theory of Computation |
| title | Dynamics and simulations of a stochastic predator-prey model with infinite delay and impulsive perturbations |
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