Spreading Speeds and Travelling Waves in Integrodifference Equations with Overcompensatory Dynamics

FieldValue
dc.contributor.authorBourgeois, Adèle
dc.date.accessioned2016-04-29T17:43:33Z
dc.date.available2016-04-29T17:43:33Z
dc.date.issued2016
dc.identifier.urihttp://hdl.handle.net/10393/34578
dc.identifier.urihttp://dx.doi.org/10.20381/ruor-5751
dc.description.abstractWe consider integrodifference equations (IDEs), which are of the form N_{t+1}(x) = \int K(x-y)F(N_t(y))dy, where K is a probability distribution and F is a growth function. It is already known that for monotone growth functions, solutions of the IDE will have spreading speeds and are sometimes in the form of travelling waves. We are interested in the case where F has a stable 2-point cycle, namely for the Ricker function and the logistic function [May, 1975]. It was claimed in [Kot, 1992] that the solution of this IDE alternates between two profiles, all the while moving with a certain speed. However, simulations revealed that not only do the profiles alternate, but the solution is a succession of two travelling objects with different speeds. Using the theory from [Weinberger, 1982], we can prove the existence of two speeds and establish their theoretical formulas. To explain the succession of travelling objects, we relate to the concept of dynamical stabilization [Malchow, 2002].
dc.language.isoen
dc.publisherUniversité d'Ottawa / University of Ottawa
dc.subjectspreading speed
dc.subjecttravelling waves
dc.subjectintegrodifference equation
dc.subjectovercompensation
dc.titleSpreading Speeds and Travelling Waves in Integrodifference Equations with Overcompensatory Dynamics
dc.typeThesis
dc.contributor.supervisorLeBlanc, Victor
dc.contributor.supervisorLutscher, Frithjof
thesis.degree.nameMSc
thesis.degree.levelMasters
thesis.degree.disciplineSciences / Science
uottawa.departmentMathématiques et statistique / Mathematics and Statistics
CollectionThèses, 2011 - // Theses, 2011 -

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