First-firing statistics of a neuron bombarded by additive coloured noise: stochastic averaging method

Abstract

The stochastic averaging method is used to evaluate the first-firing statistics of a neuron bombarded by additive coloured noise. The mathematical formulation of the first-firing statistics is established, and the first-firing probability, the probability density function of the first-firing time, and the mean first-firing time are obtained numerically. The two best-known examples of the formal spiking neuron model, a perfect integrate-and-fire neuron model and a quadratic integrate-and-fire neuron model are studied to show the application of the proposed method. All numerical results have been verified by Monte Carlo simulation. Their validity encourages further studies of other abstract neuronal models.

Keywords:

• Integrate-and-fire
• Coloured noise
• Stochastic averaging
• First-firing probability
• Mean first-firing time

AMS Subject Classification:

• 37H10
• 82C31
• 60J60

Acknowledgements

The work reported in this paper was supported by the National Natural Science Foundation of China (Grant no. 10572086) and the Foundation of ECUST (East China University of Science and Technology) for Outstanding Young Teachers (Grant no. YH0157105).