RUcore Resource Object
RUcore Resource Object
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Uniform TitleDifferential delay equations with several fixed delays
NameKennedy, Benjamin B. (author), Nussbaum, Roger (chair), Sussmann, Hector (internal member), Sontag, Eduardo (internal member), Mallet-Paret, John (outside member), Rutgers University, Graduate School - New Brunswick,
Degree Date2007
Date Created2007
SubjectMathematics,
Delay differential equations,
Functional differential equations
DescriptionWe study nonlinear autonomous real-valued differential delay equations with several fixed delays x'(t) = sum_{i=1} D F_i(x(t-d_i)), where the F_i are continuous, have nonzero limits at plus and minus infinity, and are similar (in a sense we make precise) to step functions. Our focus is on periodic solutions, and our approach is to link the above problem to an appropriately related equation y'(t) = sum_{i=1} D h_i(y(t-d_i)), where the h_i are in fact step functions.
Given a periodic solution of the second problem, we describe conditions under which this solution implies the existence of a similar periodic solution of the first problem. We also prove some results on stability of periodic solutions, and make a partial study of the global dynamics of the second problem.
Given a periodic solution of the second problem, we describe conditions under which this solution implies the existence of a similar periodic solution of the first problem. We also prove some results on stability of periodic solutions, and make a partial study of the global dynamics of the second problem.
NotePh.D.
NoteIncludes bibliographical references (p. 174-176).
Genretheses
Persistent URLhttp://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16409
LanguageEnglish
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.