Home
Resource
Counting and discounting slowly oscillating periodic solutions to Wright's equation
PDF
PDF format is widely accepted and good for printing.
Plug-in required
PDF-1(1.27 MB)
Citation & Export
View Usage Statistics
Staff View

Citation & Export
Hide

Simple citation

Jaquette, Jonathan Caleb. Counting and discounting slowly oscillating periodic solutions to Wright's equation. Retrieved from https://doi.org/doi:10.7282/T3GB27H8

Export

Click here for information about Citation Management Tools at Rutgers.

Statistics
Hide

Description

TitleCounting and discounting slowly oscillating periodic solutions to Wright's equation
NameJaquette, Jonathan Caleb (author); Mischaikow, Konstantin (chair); Nussbaum, Roger (internal member); Falk, Richard (internal member); Mireles James, Jason (outside member); Rutgers University; School of Graduate Studies
Date Created2018
Other Date2018-05 (degree)
SubjectMathematics, Delay differential equations
Extent1 online resource (ix, 152 p. : ill.)
DescriptionA 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.
NotePh.D.
NoteIncludes bibliographical references
Noteby Jonathan Caleb Jaquette
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3GB27H8
Languageeng
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
Version 8.5.5
Rutgers University Libraries - Copyright ©2024