Date of Graduation


Document Type


Degree Type



Eberly College of Arts and Sciences



Committee Chair

Kenneth Showalter

Committee Co-Chair

Larry Halliburton


Numerical and theoretical studies of the excitability boundaries for spiral waves in 2D and scroll waves in 3D are presented. The boundaries are defined by unstable wave segments, which are stabilized by using a negative feedback control algorithm. A kinematic description of the constant-size, constant-shape wave segments is presented for 2D waves. Intricate patterns of wave propagation are exhibited in a chemical reaction-diffusion system with spatiotemporal feedback. Wave behavior is controlled by feedback-regulated excitability gradients that guide propagation in specified directions. Waves reflecting or refracting are observed when interacting with a discontinuity in excitability. Wave trajectories in fixed excitability gradients are analyzed in terms of trajectory curvature and local gradient. The dependence of curvature of the trajectory and the wave speed on the gradient has also been analyzed. Spatiotemporal feedback offers wide flexibility for designing and controlling wave behavior in excitable media.*.;*This dissertation is a compound document (contains both a paper copy and a CD as part of the dissertation). The CD requires the following system requirements: Windows MediaPlayer or RealPlayer.