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Differential delay equations with several fixed delays
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Title
Differential delay equations with several fixed delays
Name
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Kennedy
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Benjamin B.
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Benjamin B. Kennedy
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Nussbaum
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Roger
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Advisory Committee
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Roger Nussbaum
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Sussmann
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Hector
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Hector Sussmann
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Eduardo
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Eduardo Sontag
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Mallet-Paret
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John
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John Mallet-Paret
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Rutgers University
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Graduate School - New Brunswick
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theses
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2007
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2007
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English
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electronic
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vi, 177 pages
Abstract
We 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.
Note
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Ph.D.
Note
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Includes bibliographical references (p. 174-176).
Subject
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Topic
Mathematics
Subject
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Topic
Delay differential equations
Subject
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Topic
Functional differential equations
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16409
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ETD_316
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doi:10.7282/T3348KSS
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ETD doctoral
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Open
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Benjamin Kennedy
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Rutgers University. Graduate School - New Brunswick
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Non-exclusive ETD license
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Author Agreement License
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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.
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