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Counting and discounting slowly oscillating periodic solutions to Wright's equation
Descriptive
TitleInfo
Title
Counting and discounting slowly oscillating periodic solutions to Wright's equation
Name
(type = personal)
NamePart
(type = family)
Jaquette
NamePart
(type = given)
Jonathan Caleb
NamePart
(type = date)
1988-
DisplayForm
Jonathan Caleb Jaquette
Role
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author
Name
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NamePart
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Mischaikow
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Konstantin
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Konstantin Mischaikow
Affiliation
Advisory Committee
Role
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chair
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Nussbaum
NamePart
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Roger
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Roger Nussbaum
Affiliation
Advisory Committee
Role
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internal member
Name
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(type = family)
Falk
NamePart
(type = given)
Richard
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Richard Falk
Affiliation
Advisory Committee
Role
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internal member
Name
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NamePart
(type = family)
Mireles James
NamePart
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Jason
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Jason Mireles James
Affiliation
Advisory Committee
Role
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outside member
Name
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NamePart
Rutgers University
Role
RoleTerm
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degree grantor
Name
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NamePart
School of Graduate Studies
Role
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school
TypeOfResource
Text
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theses
OriginInfo
DateCreated
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2018
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2018-05
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2018
Place
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xx
Language
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(type = code)
eng
Abstract
(type = abstract)
A classical example of a nonlinear delay differential equations is Wright's equation: y'(t) = −αy(t − 1)[1 + y(t)],, considering α > 0 and y(t) > −1. This thesis proves two conjectures associated with this equation: Wright's conjecture, which states that the origin is the global attractor for all α ∈ (0,π/2]; and Jones' conjecture, which states that there is a unique slowly oscillating periodic solution for α > π/2. Moreover, we prove there are no isolas of periodic solutions to Wright's equation; all periodic orbits arise from Hopf bifurcations. To prove Wright's conjecture our approach relies on a careful investigation of the neighborhood of the Hopf bifurcation occurring at α = π/2. Using a rigorous numerical integrator we characterize slowly oscillating periodic solutions and calculate their stability, proving Jones' conjecture for α ∈ [1.9, 6.0] and thereby all α ≥ 1.9. We complete the proof of Jones conjecture using global optimization methods, extended to treat infinite dimensional problems.
Subject
(authority = RUETD)
Topic
Mathematics
Subject
(authority = ETD-LCSH)
Topic
Delay differential equations
RelatedItem
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Title
Rutgers University Electronic Theses and Dissertations
Identifier
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ETD
Identifier
ETD_8761
PhysicalDescription
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (ix, 152 p. : ill.)
Note
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Ph.D.
Note
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Includes bibliographical references
Note
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by Jonathan Caleb Jaquette
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Title
School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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NjNbRU
Identifier
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doi:10.7282/T3GB27H8
Genre
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ETD doctoral
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Rights
RightsDeclaration
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The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Jaquette
GivenName
Jonathan
MiddleName
Caleb
Role
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Type
Permission or license
DateTime
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2018-04-05 16:39:58
AssociatedEntity
Name
Jonathan Jaquette
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Affiliation
Rutgers University. School of Graduate Studies
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Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical
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2018-04-05T16:35:00
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2018-04-05T16:35:00
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