Bifurcation Analysis of the Flow-Kick FitzHugh-Nagumo System of Differential Equations

Abstract

Systems modeled using differential equations often include a continuous disturbance. In reality, disturbances usually occur at discrete times. To what extent do the predictions of these continuous models still hold when the disturbance is instead applied at discrete time intervals? In this thesis, we investigate the FitzHugh-Nagumo system of differential equations with flow-kick disturbances. We use numerical continuation in MatContM to find bifurcations and study solution behavior. In particular, we investigate bifurcations that are bounded away from the continuous system in parameter space. Using numerical simulation, we observe and describe behavior in regions of parameter space where MatContM continuation fails. We also use symbolic dynamics to observe period adding bifurcations in a novel class of dynamical systems.