Date of Completion
FitzHugh-Nagumo, local minimizer, standing pulse, skew-gradient
Jeffrey M. Connors
Field of Study
Doctor of Philosophy
Reaction-diffusion systems have been primary tools for studying pattern formation. A skew-gradient system is well known to encompass a class of activator-inhibitor type reaction-diffusion systems that exhibit localized patterns such as fronts and pulses. In this dissertation, we investigate standing pulse solutions to two extensions of FitzHugh-Nagumo system that possess a skew-gradient structure. Our models exhibit additional nonlinearities that may enable the models to capture more complex behavior of standing pulse solutions. In both extensions, we employ a variational approach that involves a nonlocal term and establish the existence of standing pulse solutions with a sign change. In addition, we explore some qualitative properties of the standing pulse solutions.
Lee, Jieun, "Existence of Localized Pulse Solutions to Skew-Gradient Systems" (2020). Doctoral Dissertations. 2506.