Bursting analysis and synapse mechanism of a piece-wise constant spiking neuron model

A piece-wise constant (ab. PWC) spiking neuron model that can reproduce various neuron-like phenomena including spikings and burstings is presented. Using an analytical iterative map, it is shown that the model can exhibit spikings, burstings, and related bifurcation scenarios, which are qualitatively similar to that of standard neuron models. Also, the bifurcation scenario can be observed in an actual hardware. In addition, a synapse model for the presented neuron model is presented. It is shown that a synapse-coupled system can exhibit various synchronizations that are often observed in synapse-coupled systems of standard neuron models.