The Study Of Stochastic Resonance And The Dynamical Behavior Of A Hodgkin-Huxley Neuron

We study mainly stochastic resonance and the dynamical behavior of excitable neurons in this thesis, especially, the numerical simulation method of stochastic resonance,the effects of the changes of the amplitude and the frequency of sinusoidal signal on the mean firing rate and the interspike intervals, stochastic resonance and coherence resonance in a HH neuron. Stochastic resonance is a very important phenomenon in stochastic dynamics, the research on it plays a very important role in many scientific fields, such as information theory, optics, electrics and signal processing. The mainly used method in our study is numerical simulation. Firstly we introduce a universal second-order integration algorithm for the simulation of stochastic resonance, it applies to different kinds of noise and can be generalized to the case with many a variable. The dependence of the signal critical amplitude on its frequency and the optimal signal frequency are both related to the initial conditions.Firstly, We study the nonlinear dynamical features of a HH neuron model which includes four variables and find the frequency-dependent impendence of mean firing rate, stimulated by sinusoidal signal with the amplitude fixed, the firings can be regular or irregular. When the frequency of input approaches that of the intrinsic oscillation, the mean firing rate induced is bigger, the input signal can be effectively processed and amplified. When the frequency of signal is fixed, the distribution of the interspike intervals changes with the amplitude of input, the corresponding series of interspike intervals are of different properties, accordingly. The coherence in a neuron reflects the matching between noise and the frequency of the intrinsic oscillations, the coherence coefficient characterizing coherence resonance performs as a function of the noise strength. Stochastic resonance in a neuron describes the competition and the cooperation among the intrinsic rhythmic oscillation, the noise –induced transition and the input periodic stimulus, which results in the responses of the system behaves as functions of the noise intensities or the signal frequencies. There exists the maximal response caused by an optimal noise strength—there is a single peak in the output signal-to-noise ratio.