耦合神经元系统的放电机理及同步研究

发布时间：2018-09-12 11:30

【摘要】：生物神经元系统是由数目巨大的神经细胞组成,这些神经细胞之间通过放电进行着丰富的信息传递活动,构成了生物神经元的信息网络支持生物体的正常生命活动。神经元细胞之间传递信息是通过峰峰放电形式实现的,不同放电方式编码了不同的信息,因此可以通过研究神经元系统峰峰放电探索神经元放电规律和动力学特性。同步在自然界中无处不在,在神经元系统中两个神经元细胞之间放电同步对于神经系统的记忆、信息平衡和记忆等具有重要的意义。两个神经细胞之间的同步放电是整个神经网络的基础,所以两个神经细胞之间的耦合神经元系统同步是整个神经网络信息传递的关键。本文做了如下几方面研究:(1)基于单个神经元系统通过化学突触耦合方式得到耦合神经元系统,从单个神经元系统的稳定性出发判断了耦合神经元系统的稳定性、霍普分岔。改变系统一个参数研究了耦合系统在单参数变化下动力学特性,得到神经元系统中存在倍化分岔、加周期分岔和混沌等丰富的动力学特性。(2)给出了系统双参数平面分岔图。通过同时改变系统中两个系统参数,用不同颜色代表不同的放电周期清晰的显示了在某个特定的取值区域耦合系统的放电特性,可以为医学实验研究神经元编码方式提供理论依据。离散第三个参数观察双参数分岔的变化趋势,实现了通过多参数研究耦合神经元动力学特性。(3)从耦合神经元的耦合强度出发研究神经元的同步。首先在理论上获取了实现系统同步时耦合强度与系统参数之间的关系,在理论推导中运用了稳定等价和李雅普诺夫函数相关理论。在较弱的耦合强度下耦合神经元系统很难实现完全同步,在较强的耦合强度下则容易实现完全同步。接着研究系统参数和耦合强度共同作用下耦合系统的同步情况,给出了系统参数和耦合强度共同影响下耦合系统能否实现同步的同步图,得到每一个系统参数对耦合系统同步的影响。(4)考虑了时滞和噪声因素对耦合系统同步的影响。在耦合系统中分别加入了时滞和噪声的因素,通过数值模拟可以发现适当的时滞和外界噪声有利于耦合神经元系统达到同步,促进神经网络的信息传递,但是给出的时滞和耦合强度共同作用耦合系统同步图揭示时滞和噪声破坏系统的同步。(5)最后给出了在不同的耦合强度下耦合子系统的放电周期情况,对比两个子系统在相同耦合强度下的放电情况,揭示了耦合强度对耦合系统影响的方式。本论文研究可以全面的揭示耦合神经元系统在多参数影响的动力学性质和不同参数影响下的耦合神经元同步,可以得到如何实现耦合系统达到同步促进神经网络的信息传递。研究结果可以为医学生理实验和人工智能提供理论依据。
[Abstract]:The biological neuron system is composed of a large number of nerve cells. These nerve cells carry out abundant information transmission activities through the discharge, which constitute the information network of the biological neurons to support the normal life activities of the organism. The transmission of information between neuronal cells is realized by peak discharge, and different discharge modes encode different information. Therefore, we can explore the law and dynamic characteristics of neuronal discharge by studying the peak discharge of neuron system. Synchronization is ubiquitous in nature. In neuron system, the synchronization of discharge between two neuronal cells is of great significance to the memory, information balance and memory of the nervous system. The synchronous discharge between two nerve cells is the basis of the whole neural network, so the synchronization of the coupled neuron system between the two nerve cells is the key to the information transmission of the whole neural network. In this paper, the following studies have been done: (1) based on the chemical synaptic coupling of a single neuron system, the stability of the coupled neuron system is judged from the stability of a single neuron system, and the Hoppe bifurcation is obtained. By changing one parameter of the system, the dynamical characteristics of the coupled system with single parameter variation are studied, and the rich dynamical characteristics of the neuron system such as doubling bifurcation, periodic bifurcation and chaos are obtained. (2) the two-parameter plane bifurcation diagram of the system is given. By changing the two system parameters at the same time, the discharge characteristics of the coupled system in a particular value area are clearly displayed by different colors representing different discharge cycles. It can provide theoretical basis for the study of neural coding mode in medical experiments. The discrete third parameter observed the variation trend of two-parameter bifurcation and realized the study of coupling neuron dynamics through multi-parameter. (3) the synchronization of neurons was studied from the coupling strength of coupling neurons. Firstly, the relationship between the coupling strength and the system parameters is obtained theoretically, and the theory of stability equivalence and Lyapunov function is used in the theoretical derivation. It is difficult to achieve complete synchronization in the coupled neuron system under the weak coupling strength, but it is easy to achieve complete synchronization under the strong coupling strength. Then the synchronization of the coupled system under the joint action of the system parameters and the coupling strength is studied, and the synchronization diagram of whether the coupling system can achieve synchronization under the influence of the system parameters and the coupling strength is given. The effects of each system parameter on the synchronization of coupled systems are obtained. (4) the effects of delay and noise on the synchronization of coupled systems are considered. The factors of delay and noise are added to the coupled system respectively. Through numerical simulation, it can be found that the appropriate time delay and external noise are favorable to the synchronization of the coupled neuron system and the information transmission of the neural network can be promoted. However, the synchronization diagram of the coupled system with time-delay and coupling strength is given to reveal the synchronization between the time-delay and the noise failure system. (5) finally, the discharge period of the coupled subsystem under different coupling strengths is given. By comparing the discharge of the two subsystems under the same coupling strength, the influence of coupling strength on the coupling system is revealed. In this paper, the dynamic properties of coupled neuron system under the influence of multiple parameters and the coupling neuron synchronization under different parameters can be fully revealed, and how to achieve synchronization of coupled system to promote the information transmission of neural network can be obtained. The results can provide theoretical basis for medical physiological experiments and artificial intelligence.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：Q42;O175

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