A Review of Stochastic Models of Neuronal Dynamics: From a Single Neuron to Networks

After giving some background on neuron physiology, the classical (deterministic) models for the generation of action potentials are briefly introduced and their limitations discussed, so to motivate the need for a stochastic description of the neuronal firing activity. The more relevant stochastic models for single neuron dynamics are reviewed, with particular attention to the phenomenon of spike-frequency adaptation. Then some approaches to the modeling of network dynamics, where populations of excitatory and inhibitory neurons interact, are described. Finally, some recent models applying suitable strategies to reproduce complex neural dynamics emerging from networks of spiking neurons, such as fractional differentiation or other memory effects, are introduced as a perspective for current and future research.