First spiking dynamics of stochastic neuronal model with optimal control

Authors:
Yongjun Wu;Jianhua Peng;Ming Luo
Affiliations:
Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai, P.R. China and School of Information Science and Engineering, East China University of Science and Technology, Shangha ...;School of Information Science and Engineering, East China University of Science and Technology, Shanghai, P.R. China;School of Information Science and Engineering, East China University of Science and Technology, Shanghai, P.R. China
Venue:
ICONIP'08 Proceedings of the 15th international conference on Advances in neuro-information processing - Volume Part I
Year:
2008

Citing 4
Cited 0

Spiking Neuron Models: An Introduction

Spiking Neuron Models: An Introduction
Dynamics of the firing probability of noisy integrate-and-fire neurons

Neural Computation
Firing rate of the noisy quadratic integrate-and-fire neuron

Neural Computation
First passage time problem for the ornstein-uhlenbeck neuronal model

ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I

Quantified Score

Hi-index	0.00

Visualization

Abstract

First-spiking dynamics of optimally controlled neuron under stimulation of colored noise is investigated. The stochastic averaging principle is utilized and the model equation is approximated by diffusion process and depicted by Itô stochastic differential equation. The control problems for maximizing the resting probability and maximizing the time to first spike are constructed and the dynamical programming equations associated with the corresponding optimization problem are established. The optimal control law is determined. The corresponding backward Kolmogorov equation and Pontryagin equation are established and solved to yield the resting probability and the time to first spike. The analytical results are verified by Monte Carlo simulation. It has shown that the proposed control strategy can suppress the overactive neuronal firing activity and possesses potential application for some neural diseases treatment.