Thesis (M.Sc.). / Written for the Dept. of Physics. Title from title page of PDF (viewed 2009/06/29). Includes bibliographical references.

Theses (Ed. D.)--Marshall University, 2007. / Title from document title page. Includes abstract. Includes vitae. Document formatted into pages: contains ix, 146 pages. Bibliography: p. 122-134.

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Discrete dynamical systems can exhibit rich and interesting dynamics at lower dimensions (and co-dimensions) than that of ODE models. Classically, the minimal dimension to observe chaotic behavior in an ODE model is three; whereas it can be achieved in a one-dimensional discrete map. It is often the choice of mathematical biologists to use discrete systems as it fills many roles such as sparse data, incorporation of life cycle stages and noisy measurements. This work is analyzes a discrete time model of an infected salmon population. It provides an in-depth analysis of non-smooth bifurcations for alternate functional forms for density dependence in the growth function of a given model. These demonstrate interesting structures and chaotic behaviors with biologically feasible interpretations such as intrinsic growth rate and probability of death. The choice of density dependence function, as well as parameterization, leads to whether chaos occurs or not. / Master of Science / Often times biological processes do not happen in a continuous streamlined chain of events. We observe discrete life stages, ages, and morphological differences. Similarly, data is generally collected in discrete (and often fixed) time intervals. This work focuses on the role that population density has on the behavior of these systems. We dive into a case study for a viral infection in a salmon population. We show chaotic behavior can be observed as low as a single dimension model and discuss the biological implications. Additionally, we show that the choice of density dependence in a given infectious disease model directly impacts disease dynamics and can allow or prohibit chaotic behavior.

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This master thesis is deals with phenomenon of bifurcation in DC drive. It contains theoretical part, results of simulations and measurements of real DC drive in laboratory. The simulations was made in MATLAB, their results are bifurcation diagrams for different value of parameters. Target of measurement in laboratory was observed bifurcation on the real DC drive. Results of measurement are too transformed to bifurcation diagrams.

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