Complete Global Stability of a Metapopulation Model and Its Dynamically Consistent Discrete Models

In this paper we establish the complete global stability of a metapopulation model based on Lyapunov direct method, and the Poincare–Bendixson theorem in combination with the Bendixson–Dulac criterion. Besides, we construct nonstandard finite difference (NSFD) schemes preserving essential properties...

Full description

Saved in:
Bibliographic Details
Published in:Qualitative theory of dynamical systems 2019-08, Vol.18 (2), p.461-475
Main Authors: Dang, Quang A, Hoang, Manh Tuan
Format: Article
Language:English
Subjects:
Computer simulation
Difference and Functional Equations
Dynamic stability
Dynamical Systems and Ergodic Theory
Finite difference method
Liapunov direct method
Mathematics
Mathematics and Statistics
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-c382t-33710e841310883315b40267acae2a07764659474df7993b39a1cb60bc59881b3
cites cdi_FETCH-LOGICAL-c382t-33710e841310883315b40267acae2a07764659474df7993b39a1cb60bc59881b3
container_end_page 475
container_issue 2
container_start_page 461
container_title Qualitative theory of dynamical systems
container_volume 18
creator Dang, Quang A
Hoang, Manh Tuan
description In this paper we establish the complete global stability of a metapopulation model based on Lyapunov direct method, and the Poincare–Bendixson theorem in combination with the Bendixson–Dulac criterion. Besides, we construct nonstandard finite difference (NSFD) schemes preserving essential properties of the metapopulation model such as positivity, boundedness and monotone convergence of the solutions, equilibria and their stability. The numerical simulations confirm the validity of the obtained theoretical results and the advantages of NSFD schemes over standard finite difference schemes.
doi_str_mv 10.1007/s12346-018-0295-y
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2259975393</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2259975393</sourcerecordid><originalsourceid>FETCH-LOGICAL-c382t-33710e841310883315b40267acae2a07764659474df7993b39a1cb60bc59881b3</originalsourceid><addsrcrecordid>eNp1kD1PwzAURS0EEqXwA9gsMRv8EdvxiFIolVoxALNlpw5K5cbBdob8e1KCxMT07nDufdIB4Jbge4KxfEiEskIgTEqEqeJoPAMLIgRFjCt6PmUuOeKFwJfgKqUDxoJKRhfAVuHYe5cdXPtgjYdv2djWt3mEoYEG7lw2fegHb3IbOrgLe-eh6fZwkxNcjZ05trXxfoRV6FKbsusyXLWpjqfJHzpdg4vG-ORufu8SfDw_vVcvaPu63lSPW1SzkmbEmCTYlQVhBJclY4TbAlMhTW0cNVhKUQiuClnsG6kUs0wZUluBbc1VWRLLluBu3u1j-BpcyvoQhthNLzWlXCnJmWITRWaqjiGl6Brdx_Zo4qgJ1ieVelapJ5X6pFKPU4fOnTSx3aeLf8v_l74Bltp2IA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2259975393</pqid></control><display><type>article</type><title>Complete Global Stability of a Metapopulation Model and Its Dynamically Consistent Discrete Models</title><source>Springer Nature</source><creator>Dang, Quang A ; Hoang, Manh Tuan</creator><creatorcontrib>Dang, Quang A ; Hoang, Manh Tuan</creatorcontrib><description>In this paper we establish the complete global stability of a metapopulation model based on Lyapunov direct method, and the Poincare–Bendixson theorem in combination with the Bendixson–Dulac criterion. Besides, we construct nonstandard finite difference (NSFD) schemes preserving essential properties of the metapopulation model such as positivity, boundedness and monotone convergence of the solutions, equilibria and their stability. The numerical simulations confirm the validity of the obtained theoretical results and the advantages of NSFD schemes over standard finite difference schemes.</description><identifier>ISSN: 1575-5460</identifier><identifier>EISSN: 1662-3592</identifier><identifier>DOI: 10.1007/s12346-018-0295-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Computer simulation ; Difference and Functional Equations ; Dynamic stability ; Dynamical Systems and Ergodic Theory ; Finite difference method ; Liapunov direct method ; Mathematics ; Mathematics and Statistics</subject><ispartof>Qualitative theory of dynamical systems, 2019-08, Vol.18 (2), p.461-475</ispartof><rights>Springer Nature Switzerland AG 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-33710e841310883315b40267acae2a07764659474df7993b39a1cb60bc59881b3</citedby><cites>FETCH-LOGICAL-c382t-33710e841310883315b40267acae2a07764659474df7993b39a1cb60bc59881b3</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>Dang, Quang A</creatorcontrib><creatorcontrib>Hoang, Manh Tuan</creatorcontrib><title>Complete Global Stability of a Metapopulation Model and Its Dynamically Consistent Discrete Models</title><title>Qualitative theory of dynamical systems</title><addtitle>Qual. Theory Dyn. Syst</addtitle><description>In this paper we establish the complete global stability of a metapopulation model based on Lyapunov direct method, and the Poincare–Bendixson theorem in combination with the Bendixson–Dulac criterion. Besides, we construct nonstandard finite difference (NSFD) schemes preserving essential properties of the metapopulation model such as positivity, boundedness and monotone convergence of the solutions, equilibria and their stability. The numerical simulations confirm the validity of the obtained theoretical results and the advantages of NSFD schemes over standard finite difference schemes.</description><subject>Computer simulation</subject><subject>Difference and Functional Equations</subject><subject>Dynamic stability</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Finite difference method</subject><subject>Liapunov direct method</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1575-5460</issn><issn>1662-3592</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kD1PwzAURS0EEqXwA9gsMRv8EdvxiFIolVoxALNlpw5K5cbBdob8e1KCxMT07nDufdIB4Jbge4KxfEiEskIgTEqEqeJoPAMLIgRFjCt6PmUuOeKFwJfgKqUDxoJKRhfAVuHYe5cdXPtgjYdv2djWt3mEoYEG7lw2fegHb3IbOrgLe-eh6fZwkxNcjZ05trXxfoRV6FKbsusyXLWpjqfJHzpdg4vG-ORufu8SfDw_vVcvaPu63lSPW1SzkmbEmCTYlQVhBJclY4TbAlMhTW0cNVhKUQiuClnsG6kUs0wZUluBbc1VWRLLluBu3u1j-BpcyvoQhthNLzWlXCnJmWITRWaqjiGl6Brdx_Zo4qgJ1ieVelapJ5X6pFKPU4fOnTSx3aeLf8v_l74Bltp2IA</recordid><startdate>20190801</startdate><enddate>20190801</enddate><creator>Dang, Quang A</creator><creator>Hoang, Manh Tuan</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190801</creationdate><title>Complete Global Stability of a Metapopulation Model and Its Dynamically Consistent Discrete Models</title><author>Dang, Quang A ; Hoang, Manh Tuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-33710e841310883315b40267acae2a07764659474df7993b39a1cb60bc59881b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Computer simulation</topic><topic>Difference and Functional Equations</topic><topic>Dynamic stability</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Finite difference method</topic><topic>Liapunov direct method</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dang, Quang A</creatorcontrib><creatorcontrib>Hoang, Manh Tuan</creatorcontrib><collection>CrossRef</collection><jtitle>Qualitative theory of dynamical systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dang, Quang A</au><au>Hoang, Manh Tuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Complete Global Stability of a Metapopulation Model and Its Dynamically Consistent Discrete Models</atitle><jtitle>Qualitative theory of dynamical systems</jtitle><stitle>Qual. Theory Dyn. Syst</stitle><date>2019-08-01</date><risdate>2019</risdate><volume>18</volume><issue>2</issue><spage>461</spage><epage>475</epage><pages>461-475</pages><issn>1575-5460</issn><eissn>1662-3592</eissn><abstract>In this paper we establish the complete global stability of a metapopulation model based on Lyapunov direct method, and the Poincare–Bendixson theorem in combination with the Bendixson–Dulac criterion. Besides, we construct nonstandard finite difference (NSFD) schemes preserving essential properties of the metapopulation model such as positivity, boundedness and monotone convergence of the solutions, equilibria and their stability. The numerical simulations confirm the validity of the obtained theoretical results and the advantages of NSFD schemes over standard finite difference schemes.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s12346-018-0295-y</doi><tpages>15</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1575-5460
ispartof Qualitative theory of dynamical systems, 2019-08, Vol.18 (2), p.461-475
issn 1575-5460
1662-3592
language eng
recordid cdi_proquest_journals_2259975393
source Springer Nature
subjects Computer simulation
Difference and Functional Equations
Dynamic stability
Dynamical Systems and Ergodic Theory
Finite difference method
Liapunov direct method
Mathematics
Mathematics and Statistics
title Complete Global Stability of a Metapopulation Model and Its Dynamically Consistent Discrete Models
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T18%3A21%3A23IST&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=Complete%20Global%20Stability%20of%20a%20Metapopulation%20Model%20and%20Its%20Dynamically%20Consistent%20Discrete%20Models&rft.jtitle=Qualitative%20theory%20of%20dynamical%20systems&rft.au=Dang,%20Quang%20A&rft.date=2019-08-01&rft.volume=18&rft.issue=2&rft.spage=461&rft.epage=475&rft.pages=461-475&rft.issn=1575-5460&rft.eissn=1662-3592&rft_id=info:doi/10.1007/s12346-018-0295-y&rft_dat=%3Cproquest_cross%3E2259975393%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c382t-33710e841310883315b40267acae2a07764659474df7993b39a1cb60bc59881b3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2259975393&rft_id=info:pmid/&rfr_iscdi=true