强噪声引起的自振荡神经元的同步和李雅普诺夫指数

发布时间：2018-01-28 22:22

本文关键词： 神经元同步噪声振荡系统　出处：《华中科技大学》2007年硕士论文　论文类型：学位论文

【摘要】： 实验发现人的大脑的同一区域或者不同区域的神经元的发放都存在同步现象。单个神经元的实验也发现,当相同的类似噪声的信号刺激神经元时,发现每次实验的结果都相同,而对于确定性信号,每次实验的结果都不相同。但是对于这种同步现象的机理,至今没有完全搞清楚。为了解释这种同步现象,从而进一步认清神经如何编码,人们做了大量的理论研究。但是这些研究都侧重于弱噪声对同步的影响。而实际上,神经元中的信息是以一种不能看成弱信号、具有强烈随机性的电发放表达的,这种具有强烈随机性的发放信号的影响可以通过强随机噪声的效应讨论。所以本文中我们研究了强噪声激励下神经元的响应,并计算了李雅普诺夫指数。我们的研究发现强噪声下,不同初始条件下的振荡神经元仍然能够同步,同时得到李雅普诺夫指数的数值解为正值。第一章介绍了噪声对激发性系统、振荡系统、混沌系统的影响。第二章首先简要介绍了神经元的电活动、神经模型的建立。具体介绍了强噪声引起Adelman-Fitzhugh(AF)神经元模型同步情况和系统在不同噪声强度下李雅普诺夫指数的数值计算结果。在以往的研究中,人们强调弱噪声引起的神经元同步,发现同步时李雅普诺夫指数为负值。而实际上,神经元受到刺激不是弱刺激,而应是强刺激。但是关于强噪声下,神经元同步的研究很少。我们的研究发现强噪声下,处于不同初始条件的振荡神经元仍然同步,而且神经发放的时序非常随机,更加符合实验观察到的现象。李雅普诺夫指数的数值解为正值,而且随着噪声的增强逐渐增大,这一点也不同于以往的研究结果。第三章是拓展工作,介绍了处于阈下振荡的神经元,在强周期性信号的驱动下,输出也是周期性信号而且与输入信号的周期一致。不同初始条件下的神经元在相同的周期性信号驱动下能够同步。当继续增大输入信号的振幅时,有周期性阵发(burst)发放产生。随着输入信号的振幅的增大,每个burst中spike(发放)的数目逐渐增多。我们希望能够进一步挖掘这一结果的生理意义。第四章是结论
[Abstract]:It was found that the firing of neurons in the same or different regions of the human brain is synchronous. The experiments of single neurons also found that when the same noise-like signal stimulates neurons. It is found that the results of each experiment are the same, but for deterministic signals, the results of each experiment are different. However, the mechanism of this kind of synchronization phenomenon has not been completely understood, in order to explain the synchronization phenomenon. In order to further understand how neural coding, people have done a lot of theoretical research, but these studies are focused on the effect of weak noise on synchronization. In fact, the information in neurons is not seen as a weak signal. The effect of the strong randomness signal can be discussed by the effect of strong random noise. So we study the response of neurons under strong noise excitation in this paper. The Lyapunov exponent is calculated. Our study shows that oscillating neurons under different initial conditions can still synchronize under strong noise and the numerical solution of Lyapunov exponent is positive. In chapter 1, the effect of noise on excitation system, oscillation system and chaotic system is introduced. In the second chapter, the electrical activity of neurons is introduced briefly. The establishment of neural model. A detailed introduction of strong noise induced Adelman-Fitzhughus AFL). The synchronization of neuron model and the numerical results of Lyapunov exponent under different noise intensities have been studied in the past. People emphasize the synchronization of neurons caused by weak noise, and find that the Lyapunov exponent is negative in synchronization. In fact, the stimulation of neurons is not weak stimulation, but should be strong stimulation. We found that oscillating neurons in different initial conditions are still synchronized under strong noise, and the timing of neural firing is very random. The numerical solution of Lyapunov exponent is positive and increases with the increase of noise, which is different from previous research results. In the third chapter, we introduce the subthreshold oscillation of neurons driven by strong periodic signals. The output is also periodic and consistent with the period of the input signal. Neurons under different initial conditions can synchronize under the same periodic signal drive. When the amplitude of the input signal continues to increase. There are periodic bursts of burst.As the amplitude of the input signal increases. The number of spikes in each burst is increasing. We hope to further explore the physiological significance of this result. Chapter 4th is the conclusion
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2007
【分类号】：R35

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