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A graph-theoretic approach to the construction of Lyapunov functions for coupled systems on networks
DownloadFall 2010
For coupled systems of differential equations on networks, a graph-theoretic approach to the construction of Lyapunov functions is systematically developed in this thesis. Kirchhoff’s Matrix-Tree Theorem in graph theory plays an essential role in the approach’s development. The approach is...
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Fall 2014
We study the widespread logarithmic distribution of first significant digits and significands of data sets (referred to as Benford’s Law ) in the context of dynamical systems. Using recent tools and conditions under which a recursively defined sequence is Benford via the classical theory of...
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Spring 2016
Flows on normed spaces can be classified using flow equivalences --- maps on the space with the property that the structure of one flow is converted into the structure of another flow. Of particular interest are classifications that arise from flow equivalences that are either homeomorphisms or...