dc.rights.license | CC-BY-NC-ND | |
dc.contributor.advisor | Kuznetsov, Yu.A. | |
dc.contributor.author | Wage, B.I. | |
dc.date.accessioned | 2014-08-19T17:00:47Z | |
dc.date.available | 2014-08-19T17:00:47Z | |
dc.date.issued | 2014 | |
dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/17672 | |
dc.description.abstract | Delay Differential Equations (DDEs) appear in many applications, including neuroscience, ecology, and engineering. The analysis of one- and two-parameter families of bifurcations is based on computing normal forms of ODEs without delays describing the dynamics on center manifolds. We give an overview of so-called sun-star calculus of dual semigroups necessary to derive symbolic formulas for the critical normal form coefficients for the Hopf, Generalized Hopf, Zero-Hopf and Double Hopf bifurcations. We then discuss their implementation in the Matlab package DDE-BIFTOOL. Additionally, detection of these bifurcations was implemented. We demonstrate the new features by detecting bifurcations and computing their normal form coefficients in several DDE models. | |
dc.description.sponsorship | Utrecht University | |
dc.format.extent | 811616 | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.title | Normal form computations for Delay Differential Equations in DDE-BIFTOOL | |
dc.type.content | Master Thesis | |
dc.rights.accessrights | Open Access | |
dc.subject.keywords | delay differential equations, sun-star calculus, normal forms, continuation, numerical bifurcation analysis, software package | |
dc.subject.courseuu | Mathematical Sciences | |