Non-Normality In Scalar Delay Differential Equations

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Show simple item record Stroh, Jacob Nathaniel 2018-06-07T23:29:14Z 2018-06-07T23:29:14Z 2006
dc.description Thesis (M.S.) University of Alaska Fairbanks, 2006
dc.description.abstract Analysis of stability for delay differential equations (DDEs) is a tool in a variety of fields such as nonlinear dynamics in physics, biology, and chemistry, engineering and pure mathematics. Stability analysis is based primarily on the eigenvalues of a discretized system. Situations exist in which practical and numerical results may not match expected stability inferred from such approaches. The reasons and mechanisms for this behavior can be related to the eigenvectors associated with the eigenvalues. When the operator associated to a linear (or linearized) DDE is significantly non-normal, the stability analysis must be adapted as demonstrated here. Example DDEs are shown to have solutions which exhibit transient growth not accounted for by eigenvalues alone. Pseudospectra are computed and related to transient growth.
dc.subject Mathematics
dc.title Non-Normality In Scalar Delay Differential Equations
dc.type Thesis ms
dc.identifier.department Department of Mathematics and Statistics
dc.contributor.chair Bueler, Edward

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