Exciting threshold dependence of self-sustained spikes in excitable neurons

The dependence of self-sustained spikes on the exciting threshold is investigated by two neuron models with an initial stimulus. We find that in the sub-excitable regime of neuron, the exciting threshold is the key factor for an initial stimulus to induce self-sustained spikes, which is robust to the network structures. Furthermore, we even observe self-sustained spikes in a one-dimensional chain, in contrast to previous results stating that an external pacing or a loop structure is the necessary condition to sustain spikes. While in the excitable regime of neuron, we also find the effect of the exciting threshold, i.e. that the lower exciting threshold will result in strong firing synchronization but the higher threshold will result in weak firing synchronization. These findings may be helpful in understanding the microscopic mechanism of epileptic seizures.