The Effect of Noise on the Fitzhugh-Nagumo Neuronal Model

• Activity Number: 360
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Charles Eugene Smith*+ and Mamiko Arai
• Companies: North Carolina State University and North Carolina State University
• Keywords: neuron ; first passage time ; level crossings ; Poisson process ; stochastic differential equations

Abstract

A nonlinear system of differential equations known as the Fitzhugh-Nagumo (FN) is used to describe the physiological state of a nerve membrane. Two different kinds of noise are added to the FN model to investigate the effect of noise on the membrane. They are Gaussian white noise and Poisson noise. Gaussian white noise represents many small synaptic inputs and Poisson noise represents a few large synaptic inputs. The non-oscillatory region before and after the bifurcation region is used to distinguish between Wiener vs Poisson inputs by a hypothesis test about the mean number of level crossings. The null hypothesis is the expected level crossings of the equilbrium state by a time sampled linearized FN set of differential equations with Wiener input. The test performs well in rejecting non Wiener inputs in simulation studies, both in the linearized and nonlinear F-N model.