Polygon iterations, which can be thought of as discrete dynamical systems on the space of polygons, provide an abundance of interesting discrete dynamical systems in …
This thesis consists of four chapters on the author's research in algebraic dynamics. The first chapter introduces the main results. The second chapter is an …
Spatially localized structures, in which a spatially oscillatory pattern on a finite spatial range connects to a trivial homogeneous solution outside this range, have been …
The FitzHugh-Nagumo equations are known to admit fast traveling pulses that have monotone tails and arise as the concatenation of Nagumo fronts and backs in …
DNA stores the genetic information of almost all organisms and its integrity and stability are essential to life. Unfortunately, mutations can occur within the genome …
Many organisms need to establish spatial orientation during early development. In egg cells (oocytes) of the frog Xenopus laevis, spatial differentiation is achieved by localization …
In this thesis we address the question of pattern selection in spatially extendedsystems in the presence of stochastic noise. As a model equation, we study …
In this thesis we first study various aspects of stationary distributions of certain deterministic and stochastic dynamical systems. We look at the 30 year old …
Oscillons are spatially localized, time-periodic structures that have been observed in many natural processes, often under temporally periodic forcing. Near Hopf bifurcations, such systems can …
We investigate two different topics in discrete mathematics: the geometry of piecewise-linear surfaces and the long-term behavior of discrete dynamical systems. A regular polygon surface …
Planar target patterns are radially symmetric time-periodic structures that connect a core region with a spatially periodic traveling wave in the far field. These patterns …
Rydberg Fingerprint Spectroscopy (RFS) has been deftly applied to small molecules and shown exquisitely sensitive to global molecular structure. This has stimulated interest in its …
The studies presented in this dissertation describe and apply methods for using biplanar videoradiography to study dynamic in vivo knee motion. The techniques presented in …
