Persistent Link:
http://hdl.handle.net/10150/186368
Title:
Size-structured competition models with periodic coefficients.
Author:
Alameddine, Mona Fouad.
Issue Date:
1993
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
A system of ordinary differential equations describing the dynamics of two size structured species competing for a single unstructured resource in a chemostat is derived, under the assumption that all physiological parameters of the species are periodic functions of time. The existence of nontrivial periodic solutions of those systems is considered. Under fairly general conditions, using global bifurcation techniques, we show that a continuum of solutions bifurcate from a noncritical periodic solution of the reduced system. The positivity and stability of the bifurcating branch solutions are studied. Application to mathematical ecology is given by considering several specific cases where all system parameters are constant except some selected parameters which are taken to be small amplitude oscillations around a positive mean value. Those specific cases are studied both analytically and numerically. It is also shown, that the average size of individuals of each species is governed by a nonautonomous logistic equation whose solution under fairly general conditions approaches the unique positive periodic solution of the classical periodic logistic equation. The relationship between competitive success, coexisting species and species size is discussed. Some biological considerations are addressed including the Size-Efficiency-Hypothesis, the effects of seasonality and food limitation on the coexistence of both species.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic.; Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Cushing, James M.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleSize-structured competition models with periodic coefficients.en_US
dc.creatorAlameddine, Mona Fouad.en_US
dc.contributor.authorAlameddine, Mona Fouad.en_US
dc.date.issued1993en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractA system of ordinary differential equations describing the dynamics of two size structured species competing for a single unstructured resource in a chemostat is derived, under the assumption that all physiological parameters of the species are periodic functions of time. The existence of nontrivial periodic solutions of those systems is considered. Under fairly general conditions, using global bifurcation techniques, we show that a continuum of solutions bifurcate from a noncritical periodic solution of the reduced system. The positivity and stability of the bifurcating branch solutions are studied. Application to mathematical ecology is given by considering several specific cases where all system parameters are constant except some selected parameters which are taken to be small amplitude oscillations around a positive mean value. Those specific cases are studied both analytically and numerically. It is also shown, that the average size of individuals of each species is governed by a nonautonomous logistic equation whose solution under fairly general conditions approaches the unique positive periodic solution of the classical periodic logistic equation. The relationship between competitive success, coexisting species and species size is discussed. Some biological considerations are addressed including the Size-Efficiency-Hypothesis, the effects of seasonality and food limitation on the coexistence of both species.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academic.en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairCushing, James M.en_US
dc.contributor.committeememberLomen, David O.en_US
dc.contributor.committeememberSecomb, Timothy W.en_US
dc.identifier.proquest9408400en_US
dc.identifier.oclc720389722en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.