Periodic Solutions to Reversible Second Order Autonomous DDES in Prescribed Symmetric Nonconvex Domains

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dc.contributor.advisorBalanov, Zalman I.
dc.contributor.advisorGonzalez, Juan
dc.contributor.committeeMemberRachinskiy, Dmitry
dc.contributor.committeeMemberKrawcewicz, Wieslaw
dc.contributor.committeeMemberMakarenkov, Oleg
dc.creatorMurza, Adrian Calin
dc.date.accessioned2022-11-29T23:40:41Z
dc.date.available2022-11-29T23:40:41Z
dc.date.created2022-05
dc.date.issued2022-05-01T05:00:00.000Z
dc.date.submittedMay 2022
dc.date.updated2022-11-29T23:40:42Z
dc.description.abstractThe existence of periodic solutions to second order differential systems is a classical problem that has been studied by many authors using different methods and techniques. In this Thesis, the existence and spatio-temporal patterns of 2π-periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer O(2) × Γ × Z2-equivariant degree theory. The solutions are supposed to take their values in a prescribed symmetric domain D, while O(2) is related to the reversal symmetry combined with the autonomous form of the system. The group Γ reflects symmetries of D and/or possible coupling in the corresponding network of identical oscillaltors, and Z2 is related to the oddness of the right-hand side. Abstract results, based on the use of Gauss curvature of ∂D, Hartman-Nagumo type a priori bounds and Brouwer equivariant degree techniques, are supported by a concrete example with Γ = D8 – the dihedral group of order 16.
dc.format.mimetypeapplication/pdf
dc.identifier.uri
dc.identifier.urihttps://hdl.handle.net/10735.1/9551
dc.language.isoen
dc.subjectMathematics
dc.titlePeriodic Solutions to Reversible Second Order Autonomous DDES in Prescribed Symmetric Nonconvex Domains
dc.typeThesis
dc.type.materialtext
thesis.degree.collegeSchool of Natural Sciences and Mathematics
thesis.degree.departmentMathematics
thesis.degree.grantorThe University of Texas at Dallas
thesis.degree.namePHD

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