Neural dynamics and bifurcation analysis of piecewise linear neuron models

In this paper we study the neural dynamics and bifurcation analysis of easily implementable piecewise linear (PWL) spiking neuron models with membrane potential variables, input current, recovery variables, and parameters describing timescales. Analyses reveal that the models can reproduce six (all) kinds of bifurcation phenomena that are observed in standard biological neuron models. Moreover, these bifurcations are confirmed by time domain simulations, and along with the different phase plane geometries, these qualitative analyses provide explicit tool for the interpretation of different spiking patterns, and to guide parameter selection in PWL neuron models.