title: Geometric analysis of transient bursts.
abstract: We consider the effect of a brief stimulation from the rest state of a minimal neuronal model with multiple time scales. Such transient dynamics brings out the intrinsic bursting capabilities of the system. Our main goal is to show that a minimum of three dimensions is enough to generate spike-adding phenomena in transient responses, and that the onset of a new spike can be tracked using existing continuation packages. We take a geometric approach to illustrate how the underlying fast subsystem organises the spike adding in much the same way as for spike adding in periodic bursts, but the bifurcation analysis for spike onset is entirely different. By using a generic model, we further strengthen claims made in our earlier work that our numerical method for spike onset can be used for a broad class of systems.
authors.affiliation: Department of Mathematics, the University of Auckland, Private Bag 92019, Auckland 1142, New Zealand.
authors.forename: Hinke M
authors.initials: HM
authors.lastname: Osinga
authors.affiliation: College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF, United Kingdom.
authors.forename: Krasimira T
authors.initials: KT
authors.lastname: Tsaneva-Atanasova
mesh_terms: D006801:Humans; D016571:Neural Networks, Computer