Jump-on canard at the transition between 11-spike bursts and 12-spike bursts.

<p>The spike-adding mechanism at play in our model appears to involve canard solutions. We show here a jump-on canard, found at the transition between the 11-spike burst that was used as illustrative example throughout this paper (Figs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1011751#pcbi.1011751.g002" target="_blank">2</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1011751#pcbi.1011751.g004" target="_blank">4</a>), and a 12-spike burst obtained when increasing the pump density I<sub>max</sub>. Jump-on canards are particular solutions that connect a fast and attractive component (here when the neurons spikes), to a slow and repulsive component of the dynamics (here the short pause in the spiking within the burst), see for example [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1011751#pcbi.1011751.ref085" target="_blank">85</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1011751#pcbi.1011751.ref086" target="_blank">86</a>]. (<b>A</b>) Voltage trace during one period. (<b>B</b>) Potassium trace during one period. (<b>C</b>) Voltage trajectory superimposed onto the bifurcation diagram of the fast subsystem with respect to potassium. This trajectory follows for a while the repelling slow manifold defined by the saddle point of the fast subsystem involved in the homoclinic bifurcation (orange dashed line). I<sub>app</sub> = 0.5 μA/cm<sup>2</sup>, I<sub>max</sub> = 0.99450852625 μA/cm<sup>2</sup>.</p> <p>(PDF)</p>