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We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define excitability via singular bifurcations. In particular, we show that type I excitability is associated with a novel singular Bogdanov-Takens/SNIC… (More)

- Renato Huzak, Peter De Maesschalck
- 2014

Using techniques from singular perturbations we show that for any n ≥ 6 and m ≥ 2 there are Liénard equations { ˙ x = y − F(x), ˙ y = G(x)}, with F a polynomial of degree n and G a polynomial of degree m, having at least 2[ n−2 2 ] + [ m 2 ] hyperbolic limit cycles, where [·] denotes " the greatest integer equal or below " .

Continuation techniques have been known to successfully describe bifurcation diagrams appearing in slow-fast systems with more than one slow variable (see eg. [12]). In this paper we investigate the usefulness of numerical continuation techniques dealing with some solved and some open problems in the study of planar singular perturbations. More precisely,… (More)

- Peter De Maesschalck, Nikola Popovi´c, Tasso J Kaper
- 2009

In ordinary differential equations of singular perturbation type, the dynamics of solutions near saddle-node bifurcations of equilib-ria are rich. Canard solutions can arise, which, after spending time near an attracting equilibrium, stay near a repelling branch of equilibria for long intervals of time before finally returning to a neighborhood of the… (More)

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