An Investigation into the Colored Stochastic Hodgkin-Huxley Equations Under Time Varying Input Currents

ABSTRACT: In recent years, it has been argued and shown experimentally that ion channel noise in neurons can cause fundamental effects on the neuron’s dynamical behavior. Most profoundly, ion channel noise was seen to be able to cause spontaneous firing and stochastic resonance. It was recently found by Güler (2011) that a non-trivially persistent cross correlation regard position among thе transmembrane voltage fluctuations and the element of open channel fluctuations attributed to the gate multiplicity. This non-trivial phenomenon was found to be playacting an essential important role for the elevation of excitability and spontaneous firing in the small size cell. Furthermore, the same phenomenon was found to be enhancing thе spike coherence significantly. More recently, thе effects of thе above cross correlation persistency was modeled; by thе same author M. Güler (2013), through inserting some colored noise terms inside thе conductances in thе stochastic Hodgkin Huxley equation. In this thesis, we study the above colored stochastic equations under time varying periodic input currents. Our investigation reveals that above a critical value of the input frequency and also below a certain amplitude value, the colored terms play a very prominent role on the firing statistics. Keywords: colored noise, channel gate, Ion channel, small size membrane, channel noise, Stochastic Hodgkin-Huxley equations. ……………………………………………………………………………………………………………………………………………………………………………………………………………………