Geometric analysis of transient bursts
Hinke M. Osinga, and Krasimira T. Tsaneva-Atanasova
Abstract
We consider the effect of a short-time perturbation from the rest state of a stylised neuronal model with multiple time scales. Such transient dynamics brings out the intrisic 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.
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