Stochastic neuronal models with realistic synaptic inputs and oscillatory inputs

Abstract

The Poisson process driven stochastic models of the neural activity and their diffusion approximation are studied. Two main studies are presented here: stochastic models driven by nonhomogeneons Poisson process with oscillatory intensity, and double compartment model with realistic synaptic inputs. The “phase lock” and the “amplitude lock” behaviour was observed in the model with oscillatory inputs and strong dependence on the initial phase after reset the membrane potential. Introducing the realistic synaptic input to the stochastic models opens new class of neuronal models: it has significant influence on all statistic parameters and the model behaviour. The double compartment model with realistic synaptic inputs is able to produce the bursting activity and this mechanism is described.