2012 Volume 3 Issue 4 Pages 557-572
A piece-wise constant (ab. PWC) spiking neuron model (ab. PWN) has a PWC vector field with a state-dependent reset and is designed to reproduce responses of neurons. Based on analysis techniques for discontinuous ODEs, the dynamics of inhibitory responses of the PWN can be reduced into an one-dimensional iterative map analytically. Using the map, it is shown that the PWN can reproduce bifurcation scenarios of inhibitory responses, which are qualitatively similar to those of the Izhikevich model. In addition, a typical bifurcation scenario can be observed in an actual hardware.