Figure 2

A Theta neuron (7) with phase \(\theta _{k}\) subject to constant input I undergoes a saddle node bifurcation on an invariant circle (SNIC) as the quantity \(\iota_{k}=\eta_{k}+\kappa I\) is varied. The neuron spikes if its phase \(\theta_{k}\) crosses \(\theta_{k}=\pi\). If \(\iota_{k}<0\) the Theta neuron is excitable: the phase will relax to the stable equilibrium and a phase perturbation of the phase across the saddle equilibrium (its threshold) will lead to a single spike before returning to equilibrium. For \(\iota_{k}>0\), the Theta neuron is spiking periodically