Date of Award
College of Science
Type of Degree
Bonita A. Lawrence
Ralph W. Oberste-Vorth
In this thesis we use the theory of dynamic equations on time scales to understand the changes in dynamics between difference and differen- tial equations by parameterizing the underlying domains. To illustrate where and how these changes occur, we then construct a bifurcation diagram for a simple family of dynamic equations. However, these results are only true if we can move continuously through our domains, i.e, the time scales. In the last part of this thesis, we define what it means to have a convergent sequence of time scales. Then we use this definition to prove that the limit of solutions over a convergent sequence of time scales converges to a solution over the limit time scale.
Differentiable dynamical systems.
Hall, Kelli J., "Dynamic Equations on Changing Time Scales: Dynamics of Given Logistic Problems, Parameterization, and Convergence of Solutions" (2005). Theses, Dissertations and Capstones. 618.