An Investigation of the Neuronal Dynamics Under Noisy Rate Functions

ABSTRACT: In latest years, it has been argued theoretically both by experiments and by numerical simulations that noise of ion channel in neurons effect on the dynamical behavior of neuron when the size of membrane area is limited. Different models that extend the Hodgkin-Huxley equations into stochastic differential equations to capture the effects of ion channel noise analytically have been put forward: the Fox-Lu model, the Linaro-Storace-Giugliano model, and the Güler model. Moreover, very recently it has been argued by Güler that the rate functions for the opening and closing of gates are under the influence of noise in small size neurons. In this thesis, the neuronal dynamics with subject to noise in the rate functions will be investigated thoroughly. The investigation will employ the exact Markov simulations and the above analytical models. Results from these models will be presented comparatively. The study aims at presenting a more detailed account on the phenomenon already outlined by Güler recently. Keywords: Ion Channels, Channel Noise, Colored Noise, The Channel Crossing, Small-sized Dice, Stochastic Hodgkin-Huxley. …………………………………………………………………………………………………………………………