Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate

Detalhes bibliográficos
Autor(a) principal: Wang,Xia
Data de Publicação: 2011
Outros Autores: Guo,Zhen, Song,Xinyu
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000200008
Resumo: In this paper, we consider the pest management model with spraying microbial pesticide and releasing the infected pests, and the infected pests have the function similar to the microbial pesticide and can infect the healthy pests, further weaken or disable their prey function till death. By using the Floquet theory for impulsive differential equations, we show that there exists a globally asymptotically stable pest eradication periodic solution when the impulsive period τ < τmax, we further prove that the system is uniformly permanent if the impulsive period τ &gt; τmax. Finally, by means of numerical simulation, we showthatwith the increaseof impulsive period, the system displays complicated behaviors.
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spelling Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence ratepest-management modelimpulsive effectextinctionpermanenceIn this paper, we consider the pest management model with spraying microbial pesticide and releasing the infected pests, and the infected pests have the function similar to the microbial pesticide and can infect the healthy pests, further weaken or disable their prey function till death. By using the Floquet theory for impulsive differential equations, we show that there exists a globally asymptotically stable pest eradication periodic solution when the impulsive period τ < τmax, we further prove that the system is uniformly permanent if the impulsive period τ &gt; τmax. Finally, by means of numerical simulation, we showthatwith the increaseof impulsive period, the system displays complicated behaviors.Sociedade Brasileira de Matemática Aplicada e Computacional2011-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000200008Computational &amp; Applied Mathematics v.30 n.2 2011reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022011000200008info:eu-repo/semantics/openAccessWang,XiaGuo,ZhenSong,Xinyueng2011-07-27T00:00:00Zoai:scielo:S1807-03022011000200008Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2011-07-27T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate
title Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate
spellingShingle Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate
Wang,Xia
pest-management model
impulsive effect
extinction
permanence
title_short Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate
title_full Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate
title_fullStr Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate
title_full_unstemmed Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate
title_sort Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate
author Wang,Xia
author_facet Wang,Xia
Guo,Zhen
Song,Xinyu
author_role author
author2 Guo,Zhen
Song,Xinyu
author2_role author
author
dc.contributor.author.fl_str_mv Wang,Xia
Guo,Zhen
Song,Xinyu
dc.subject.por.fl_str_mv pest-management model
impulsive effect
extinction
permanence
topic pest-management model
impulsive effect
extinction
permanence
description In this paper, we consider the pest management model with spraying microbial pesticide and releasing the infected pests, and the infected pests have the function similar to the microbial pesticide and can infect the healthy pests, further weaken or disable their prey function till death. By using the Floquet theory for impulsive differential equations, we show that there exists a globally asymptotically stable pest eradication periodic solution when the impulsive period τ < τmax, we further prove that the system is uniformly permanent if the impulsive period τ &gt; τmax. Finally, by means of numerical simulation, we showthatwith the increaseof impulsive period, the system displays complicated behaviors.
publishDate 2011
dc.date.none.fl_str_mv 2011-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000200008
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000200008
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1807-03022011000200008
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational &amp; Applied Mathematics v.30 n.2 2011
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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