Global existence and asymptotic behavior of a model for biological control of invasive species via supermale introduction

Handle URI:
http://hdl.handle.net/10754/562518
Title:
Global existence and asymptotic behavior of a model for biological control of invasive species via supermale introduction
Authors:
Parshad, Rana ( 0000-0001-7443-8927 ) ; Kouachi, Saïd; Gutiérrez, Juan B.
Abstract:
The purpose of this manuscript is to propose a model for the biological control of invasive species, via introduction of phenotypically modified organisms into a target population. We are inspired by the earlier Trojan Y Chromosome model [J.B. Gutierrez, J.L. Teem, J. Theo. Bio., 241(22), 333-341, 2006]. However, in the current work, we remove the assumption of logisticgrowth rate, and do not consider the addition of sex-reversed supermales. Also the constant birth and death coefficients, considered earlier, are replaced by functionally dependent ones. In this case the nonlinearities present serious difficulties since they change sign, and the components of the solution are not a priori bounded, in some Lp-space for p large, to permit theapplication of the well known regularizing effect principle. Thus functional methods to deducethe global existence in time, for the system in question, are not applicable. Our techniques are based on the Lyapunov functional method. We prove global existence of solutions, as well asexistence of a finite dimensional global attractor, that supports states of extinction. Our analytical finding are in accordance with numerical simulations, which we also present. © 2013 International Press.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
International Press
Journal:
Communications in Mathematical Sciences
Issue Date:
2013
DOI:
10.4310/CMS.2013.v11.n4.a4
Type:
Article
ISSN:
15396746
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorParshad, Ranaen
dc.contributor.authorKouachi, Saïden
dc.contributor.authorGutiérrez, Juan B.en
dc.date.accessioned2015-08-03T10:41:06Zen
dc.date.available2015-08-03T10:41:06Zen
dc.date.issued2013en
dc.identifier.issn15396746en
dc.identifier.doi10.4310/CMS.2013.v11.n4.a4en
dc.identifier.urihttp://hdl.handle.net/10754/562518en
dc.description.abstractThe purpose of this manuscript is to propose a model for the biological control of invasive species, via introduction of phenotypically modified organisms into a target population. We are inspired by the earlier Trojan Y Chromosome model [J.B. Gutierrez, J.L. Teem, J. Theo. Bio., 241(22), 333-341, 2006]. However, in the current work, we remove the assumption of logisticgrowth rate, and do not consider the addition of sex-reversed supermales. Also the constant birth and death coefficients, considered earlier, are replaced by functionally dependent ones. In this case the nonlinearities present serious difficulties since they change sign, and the components of the solution are not a priori bounded, in some Lp-space for p large, to permit theapplication of the well known regularizing effect principle. Thus functional methods to deducethe global existence in time, for the system in question, are not applicable. Our techniques are based on the Lyapunov functional method. We prove global existence of solutions, as well asexistence of a finite dimensional global attractor, that supports states of extinction. Our analytical finding are in accordance with numerical simulations, which we also present. © 2013 International Press.en
dc.publisherInternational Pressen
dc.subjectGlobal attractoren
dc.subjectGlobal existenceen
dc.subjectInvasive species managementen
dc.subjectLyapunov functionalen
dc.subjectReaction-diffusion systemen
dc.titleGlobal existence and asymptotic behavior of a model for biological control of invasive species via supermale introductionen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalCommunications in Mathematical Sciencesen
dc.contributor.institutionDepartment of Mathematics, College of Science, Qassim University, P.O. Box 6644, Al-Gassim, Buraydah 51452, Saudi Arabiaen
dc.contributor.institutionDepartment of Mathematics and Institute of Bioinformatics, University of Georgia, Athens, GA 30602, United Statesen
kaust.authorParshad, Ranaen
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