The 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. / Master of Science / There are many systems in our society which are vital, and require quantitative analysis. These include population dynamics, transportation, and energy. To answer research questions about these systems, one may construct a mathematical model of the system and conduct simulations. It is important to define both the mathematical model and the simulation model in order to better understand the source of errors, or to be confident in the validity of the models. One source of error may be in parameters of our simulation model. It can be difficult to gather reliable and precise data, especially in massively interacting systems. Thus we would like to know that there is a range of values which will result in similar outcomes. Stability results can give us this assurance. This paper mainly focuses on stability results in graph dynamical systems (GDS), which is the underlying mathematical model of many simulation models, especially ones with a networked structure.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/83604 |
| Date | 20 June 2018 |
| Creators | Mcnitt, Joseph Andrew |
| Contributors | Mathematics, Mortveit, Henning S., Floyd, William J., Borggaard, Jeffrey T. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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