A novel piece-wise constant analog spiking neuron model and its neuron-like excitabilities

A novel analog spiking neuron model which has a piece-wise constant (ab. PWC) vector field and can be implemented by a simple electronic circuit is proposed. Using theories on discontinuous ODEs, the dynamics of the proposed model can be reduced into a one-dimensional return map analytically. Using the return map, it is shown that the proposed model can exhibit various neuron-like behaviors and bifurcations. It is also shown that the model can reproduce not only the individual neuron-like behaviors and bifurcations but also relations among them that are typically observed in biological and model neurons.