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

Authors:
Yongjun Wu;Wang Fang;Jianhua Peng;Ming Luo
Affiliations:
College of Information Science and Engineering, East China University of Science and Technology, Shanghai, P.R. China;Hangzhou Yiheng Technologies Co. Ltd., Hangzhou, P.R. China;College of Information Science and Engineering, East China University of Science and Technology, Shanghai, P.R. China;College of Information Science and Engineering, East China University of Science and Technology, Shanghai, P.R. China
Venue:
International Journal of Computer Mathematics - Computer Mathematics in Dynamics and Control
Year:
2008

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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.