Date of Award
Spring 4-22-2026
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
May 2026
Department
Mathematics and Statistics
College Granting Degree
Charles E. Schmidt College of Science
Department Granting Degree
Mathematics and Statistics
Degree Name
Doctor of Philosophy (PhD)
Thesis/Dissertation Advisor [Chair]
Vincent Naudot
Abstract
The field of delay differential equations (DDEs) concerns the study of systems whose evolution depends on certain past states of the system. Of particular interest are the state-dependent DDEs, whose delay terms are non-constant and depend on the current state itself. In this thesis, we provide rigorous solution-finding techniques for a certain class of one-dimensional state-dependent DDEs, as well as a state-dependent delayed Van der Pol equation. This technique is inspired by the classical Picard-Lindelof theorem and is successful in proving the existence and uniqueness of orbits in such systems under certain reasonable restrictions. We then employ the Lagrange-Chebyshev interpolating operator to frame our results in the computational setting, allowing us to algorithmically obtain periodic orbits of the systems in question. These algorithms are based on the Newton-Kantorovich theorem and the resulting illustrations and numerics are discussed in detail.
Recommended Citation
Corbett, Noah, "A COMPUTATIONAL APPROACH TO PERIODIC ORBITS OF STATE-DEPENDENT DELAY DIFFERENTIAL EQUATIONS" (2026). Electronic Theses and Dissertations. 251.
https://digitalcommons.fau.edu/etd_general/251