  In this paper, we propose a shot noise-based leaky integrated and firing
neuron model and provide a detailed analysis of the performance of this model
compared to the traditional diffusion approximated model. In theoretical
neuroscience, there are three general neuron models in the field: Compartmental
neuron model is a conductance-based model, in which it views the biological
neurons as a large circuit. The problem of this model comes from its structural
complexity and the number of its free parameters; Leaky integrated and firing
model is a more flexible model due to the special design called
threshold-resetting, in which the voltage of the neuron is reset after reaching
the threshold. This model is proposed as an alternative to the compartment
model to provide a more biologically realistic model that can capture spike
timing behaviors that are observed in experiments. In addition to that, it is
more computationally efficient since it has much less free parameters; Firing
rate-based neuron model uses the firing rate of the neuron as the coupling
terms in the coupled neuronal network models. Models of this kind can be easily
analyzed on the network level. Theoretical analysis for this model proves the
existence of phase transition and shows that the computational capacity is
boosted in the chaotic regime.
