Joint work with: Jakub Nowacki and Krasimira Tsaneva-Atanasova, University of Bristol, UK

We show how tools from dynamical systems can be used to analyse transient bursting behaviour in a simplified five-dimensional excitable neuron model subject to a short current injection. We use one-parameter continuation of the perturbed orbit segments, formulated as a well-posed boundary value problem, to investigate the phenomenon that additional spikes are added to the transient response as a parameter is varied. By exploiting a natural time-scale separation, we obtain insight into the spike-adding mechanism via geometric singular perturbation theory. More specifically, spike adding occurs through a canard-like transition, where the transient response involves unstable sheets of the critical manifold.