【作者】 唐初明；

【导师】 唐翌；

【作者基本信息】 湘潭大学 ， 理论物理， 2004， 硕士

【摘要】 本论文主要研究了随机共振和可兴奋性神经元的动力学行为,重点研究了随机共振的数值模拟方法、正弦信号的振幅和频率变化对神经元的平均发放率和峰峰间期分布产生的影响以及神经元中的相干共振和随机共振。随机共振是随机动力学中一种非常重要的现象,关于它的研究在信息理论、光学、电学及信号处理许多领域中都具有重要意义。本文主要采用数值模拟的方法进行研究。我们推导了一种用于随机共振数值模拟的通用二阶积分方法,它适用于不同类型的噪声,并且可以推广到含有多个变量的情况。我们首先研究了含四个变量的HH神经元的非线性动力学特征,发现其平均发放率具有频率依赖性,在振幅一定的正弦信号刺激下,神经元产生的发放既有规则的,也有不规则的。当信号的频率接近其本征振荡频率时,神经元产生的平均发放率较大,输入信号就能被有效地处理和放大。当信号频率一定时,神经元的峰峰间期分布随信号振幅而改变,对应的峰峰间期序列具有不同的特点。信号的临界振幅对其频率的依赖关系、信号最佳频率均与初始条件有关。神经元中的相干共振反映了噪声与神经元的本征振荡频率之间的一种匹配,描述相干共振的相干系数是噪声强度的函数。神经元中的随机共振描述了节律振荡、噪声诱导的穿越以及输入的周期信号等因素的竞争与协作,其结果导致系统对信号的响应表现为噪声强度或信号频率的函数,存在着最佳的噪声强度使得系统的响应最大—输出的信噪比取单一的峰值。更多还原

【Abstract】 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, <WP=5>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.更多还原