Stability in Graph Dynamical Systems

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dc.contributor.authorMcnitt, Joseph Andrewen
dc.contributor.committeechairMortveit, Henning S.en
dc.contributor.committeememberFloyd, William J.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2018-06-21T08:01:20Zen
dc.date.available2018-06-21T08:01:20Zen
dc.date.issued2018-06-20en
dc.description.abstractThe underlying mathematical model of many simulation models is graph dynamical systems (GDS). This dynamical system, its implementation, and analyses on each will be the focus of this paper. When using a simulation model to answer a research question, it is important to describe this underlying mathematical model in which we are operating for verification and validation. In this paper we discuss analyses commonly used in simulation models. These include sensitivity analyses and uncertainty quantification, which provide motivation for stability and structure-to-function research in GDS. We review various results in these areas, which contribute toward validation and computationally tractable analyses of our simulation model. We then present two new areas of research - stability of transient structure with respect to update order permutations, and an application of GDS in which a time-varying generalized cellular automata is implemented as a simulation model.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:15291en
dc.identifier.urihttp://hdl.handle.net/10919/83604en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectStabilityen
dc.subjectSensitivityen
dc.subjectGraph dynamical systemsen
dc.subjectNetworksen
dc.subjectTuta Absolutaen
dc.titleStability in Graph Dynamical Systemsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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