Fig. 7

Orbit of a periodic travelling wave. Parameters as in Fig. 5, with \(\varDelta= 450\), \(c = 0.0669\), \(n_{h}(0) = 0.3815\) and \(\xi_{1} = 225.4223\). The travelling wave starts at \(\xi=0\) where \(V=V_{r}\) is clamped and \(n_{h}\) evolves according to (29) until \(\xi= \tau_{\mathrm{R}}\) and the system is released from the refractory period (blue line). Then it evolves clockwise according to (26) with \(\mu= 0\) until \(V(\tau_{\mathrm{R}} + \xi_{1})=V_{+}\) when it switches (red line) to \(\mu=+\) (green line). The orbit ends when \(V=V_{\text{th}}\) and V is reset. The green horizontal line for \(V > V_{\text{th}}\) is not part of the solution. It is simply a marker for the spiking event (and the model does not generate an explicit shape for an action potential). Black dotted lines represent (from left to right) \(V=V_{-}\), \(V=V_{+}\) and \(V=V_{\text{th}}\)