Chaotic states caused by discontinuous resetting process in spiking neuron model

Spiking neuron models, which can realize diverse kinds of neural coding by describing spiking activity of membrane potential, have been widely utilized. Among these models, several hybrid spiking neuron models, which combine continuous spike-generation mechanisms and discontinuous resetting process after spiking, have been proposed as a simple transition scheme for membrane potential between spike and hyperpolarization. Izhikevich neuron model as this kind of model can reproduce many spiking patterns. It has also become clear that this model has various kinds of bifurcation and routes to chaos under the effect of the state dependent jump in the resetting process. In response to this situation, we have further gotten interested in the relation between chaotic behaviors and the state dependent jump. In this paper, we approach the subject from the comparison of spiking neuron models without the resetting process and with it. We first adopt a continuous two-dimensional spiking neuron model where the orbit at spiking state does not exhibit the divergent behavior and next insert the resetting process to it.