Noise induced phenomena in jump diffusion models for single neuron spike activity

Noise plays an important role in neural transmission and stochastic neuronal models can be employed to help the understanding of coding principles. The attempt to detect instances, where the noise plays a positive role increasing the reliability of the signal or synchronizing the spike trains of different neurons, requests the use of suitable biologically compatible mathematical models. A contribution in this direction is the use of jump-diffusion models to describe the time evolution of membrane potential of some neurons in the brain. This approach can be biologically justified with arguments based on different weights for the synaptic contribution impinging the neuron in any point of the membrane and synapses acting near the trigger zone. The simple observation of the existence of two types of noises in the resulting models suggests the existence of interactions between them and hence the possible occurrence of optimal noise values that could determine multimodal distributions despite the total absence of periodic inputs.