Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays

In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of...

Full description

Saved in:
Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2007-03, Vol.53 (5), p.770-788
Main Authors: Xu, Rui, Chaplain, M.A.J., Davidson, F.A.
Format: Article
Language:English
Subjects:
Computer simulation
Convergence
Delay
Energy use
Gestation
Global convergence
Mathematical analysis
Mathematical models
Nonlocal delay
Predators
Reaction–diffusion
Stage structure
Steady-state solution
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c400t-e277008e2147c6ada20b24200a92f1c51e3553721a5e59821b99558d8f84562b3
cites cdi_FETCH-LOGICAL-c400t-e277008e2147c6ada20b24200a92f1c51e3553721a5e59821b99558d8f84562b3
container_end_page 788
container_issue 5
container_start_page 770
container_title Computers & mathematics with applications (1987)
container_volume 53
creator Xu, Rui
Chaplain, M.A.J.
Davidson, F.A.
description In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method. Numerical simulations are carried out to illustrate the main results.
doi_str_mv 10.1016/j.camwa.2007.02.002
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_29817571</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0898122107000302</els_id><sourcerecordid>1082199810</sourcerecordid><originalsourceid>FETCH-LOGICAL-c400t-e277008e2147c6ada20b24200a92f1c51e3553721a5e59821b99558d8f84562b3</originalsourceid><addsrcrecordid>eNqNkb1u2zAURokiAer8PEEWTkEXKZdXokgNHQqjTQsEyJLMBE1dpXRl0SGlBN76Dn3DPknoOrPRhbwgzvcBl4exKwGlANHcrEtnN6-2RABVApYA-IEthFZVoZpGn7AF6FYXAlF8ZGcprQGgrhAW7NftEFZ24C6MLxSfaHTEQ88tj2Td5MP49_efzvf9nPLMt5E6O4WYH_O445vQ0cBf_fSTp8k-UT7j7KY5Erdjx8cwDsHl9kzZXbpgp70dEl2-3-fs8dvXh-X34u7-9sfyy13haoCpIFQKQBOKWrnGdhZhhXVezbbYCycFVVJWCoWVJFuNYtW2UupO97qWDa6qc3Z96N3G8DxTmszGJ0fDYEcKczLYaqGkEhn8dBQUkNvbTMN_oigaldHqgLoYUorUm230Gxt3GTJ7XWZt_ukye10G0GRdOfX5kKL8My-eoknO73V0PpKbTBf80fwbZNOgoA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1082192167</pqid></control><display><type>article</type><title>Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays</title><source>ScienceDirect Freedom Collection 2022-2024</source><creator>Xu, Rui ; Chaplain, M.A.J. ; Davidson, F.A.</creator><creatorcontrib>Xu, Rui ; Chaplain, M.A.J. ; Davidson, F.A.</creatorcontrib><description>In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method. Numerical simulations are carried out to illustrate the main results.</description><identifier>ISSN: 0898-1221</identifier><identifier>EISSN: 1873-7668</identifier><identifier>DOI: 10.1016/j.camwa.2007.02.002</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Computer simulation ; Convergence ; Delay ; Energy use ; Gestation ; Global convergence ; Mathematical analysis ; Mathematical models ; Nonlocal delay ; Predators ; Reaction–diffusion ; Stage structure ; Steady-state solution</subject><ispartof>Computers &amp; mathematics with applications (1987), 2007-03, Vol.53 (5), p.770-788</ispartof><rights>2007 Elsevier Ltd</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c400t-e277008e2147c6ada20b24200a92f1c51e3553721a5e59821b99558d8f84562b3</citedby><cites>FETCH-LOGICAL-c400t-e277008e2147c6ada20b24200a92f1c51e3553721a5e59821b99558d8f84562b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Xu, Rui</creatorcontrib><creatorcontrib>Chaplain, M.A.J.</creatorcontrib><creatorcontrib>Davidson, F.A.</creatorcontrib><title>Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays</title><title>Computers &amp; mathematics with applications (1987)</title><description>In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method. Numerical simulations are carried out to illustrate the main results.</description><subject>Computer simulation</subject><subject>Convergence</subject><subject>Delay</subject><subject>Energy use</subject><subject>Gestation</subject><subject>Global convergence</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Nonlocal delay</subject><subject>Predators</subject><subject>Reaction–diffusion</subject><subject>Stage structure</subject><subject>Steady-state solution</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNqNkb1u2zAURokiAer8PEEWTkEXKZdXokgNHQqjTQsEyJLMBE1dpXRl0SGlBN76Dn3DPknoOrPRhbwgzvcBl4exKwGlANHcrEtnN6-2RABVApYA-IEthFZVoZpGn7AF6FYXAlF8ZGcprQGgrhAW7NftEFZ24C6MLxSfaHTEQ88tj2Td5MP49_efzvf9nPLMt5E6O4WYH_O445vQ0cBf_fSTp8k-UT7j7KY5Erdjx8cwDsHl9kzZXbpgp70dEl2-3-fs8dvXh-X34u7-9sfyy13haoCpIFQKQBOKWrnGdhZhhXVezbbYCycFVVJWCoWVJFuNYtW2UupO97qWDa6qc3Z96N3G8DxTmszGJ0fDYEcKczLYaqGkEhn8dBQUkNvbTMN_oigaldHqgLoYUorUm230Gxt3GTJ7XWZt_ukye10G0GRdOfX5kKL8My-eoknO73V0PpKbTBf80fwbZNOgoA</recordid><startdate>20070301</startdate><enddate>20070301</enddate><creator>Xu, Rui</creator><creator>Chaplain, M.A.J.</creator><creator>Davidson, F.A.</creator><general>Elsevier Ltd</general><scope>6I.</scope><scope>AAFTH</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>20070301</creationdate><title>Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays</title><author>Xu, Rui ; Chaplain, M.A.J. ; Davidson, F.A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c400t-e277008e2147c6ada20b24200a92f1c51e3553721a5e59821b99558d8f84562b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Computer simulation</topic><topic>Convergence</topic><topic>Delay</topic><topic>Energy use</topic><topic>Gestation</topic><topic>Global convergence</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Nonlocal delay</topic><topic>Predators</topic><topic>Reaction–diffusion</topic><topic>Stage structure</topic><topic>Steady-state solution</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>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; 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>Computers &amp; mathematics with applications (1987)</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>Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays</atitle><jtitle>Computers &amp; mathematics with applications (1987)</jtitle><date>2007-03-01</date><risdate>2007</risdate><volume>53</volume><issue>5</issue><spage>770</spage><epage>788</epage><pages>770-788</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method. Numerical simulations are carried out to illustrate the main results.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.camwa.2007.02.002</doi><tpages>19</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0898-1221
ispartof Computers & mathematics with applications (1987), 2007-03, Vol.53 (5), p.770-788
issn 0898-1221
1873-7668
language eng
recordid cdi_proquest_miscellaneous_29817571
source ScienceDirect Freedom Collection 2022-2024
subjects Computer simulation
Convergence
Delay
Energy use
Gestation
Global convergence
Mathematical analysis
Mathematical models
Nonlocal delay
Predators
Reaction–diffusion
Stage structure
Steady-state solution
title Global convergence of a reaction–diffusion predator–prey model with stage structure and nonlocal delays
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T05%3A19%3A19IST&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=Global%20convergence%20of%20a%20reaction%E2%80%93diffusion%20predator%E2%80%93prey%20model%20with%20stage%20structure%20and%20nonlocal%20delays&rft.jtitle=Computers%20&%20mathematics%20with%20applications%20(1987)&rft.au=Xu,%20Rui&rft.date=2007-03-01&rft.volume=53&rft.issue=5&rft.spage=770&rft.epage=788&rft.pages=770-788&rft.issn=0898-1221&rft.eissn=1873-7668&rft_id=info:doi/10.1016/j.camwa.2007.02.002&rft_dat=%3Cproquest_cross%3E1082199810%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c400t-e277008e2147c6ada20b24200a92f1c51e3553721a5e59821b99558d8f84562b3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1082192167&rft_id=info:pmid/&rfr_iscdi=true