复杂脑网络神经系统的相同步研究

发布时间：2019-06-25 19:22

【摘要】：脑是支配人类活动的司令部和信息中心，神经系统承担感受外界刺激，产生、处理、传导和整合信号，进行高级认知功能活动，，以及从事运动控制等重要功能。神经系统动力学结合复杂网络相关理论研究脑网络神经系统的消息处理和传递机制是近年兴起的新的研究方法，通过这种研究方法可以更好的认识和理解脑神经网络的认知行为。研究表明真实脑神经系统网络具有明显的小世界网络特性。随着研究不断深入，发现真实脑神经系统网络也具有无标度网络特性。本文根据复杂网络相关理论建立了小世界神经系统网络模型和无标度神经系统网络模型，把网络的节点定义为神经元，采用HH神经元模型描述网络节点的动力系统状态，研究了这两种脑神经系统复杂网络模型的相同步。首先，介绍神经系统动力学的基础知识和复杂网络的基础理论。详细描述神经系统动力学中常用的几种神经系统动力学数学模型；介绍了目前神经系统动力学主要研究的三个方向即随机共振、相干共振和神经系统同步动力学。其次，根据神经系统动力学数学模型中的HH神经元模型，基于复杂网络理论构建WS小世界神经系统网络，并研究此网络模型的相同步。采用解析信号逼近的方法定义小世界神系统网络节点的相位，把神经元的膜电压作为系统的状态变量，通过计算网络平均频率来判断网络的相同步状态。应用matlab进行数值仿真，对仿真图像进行分析，得出小世界神经网络的相同步与网络的耦合度和重连概率有密切的联系。然后，结合复杂网络理论和神经系统动力学数学模型中的HH神经元模型，构建BA无标度神经网络，并研究此网络模型的相同步。在matlab环境下进行仿真，通过仿真结果的分析得出当耦合强度超出临界耦合强度时，网络中就会出现相同步现象；在构建无标度神经系统网络过程中，每加入一个神经元节点而与网络中己有节点相连的边数m也决定了网络的同步性能，m越大，网络同步性能越好。
[Abstract]:The brain is the headquarters and information center that dominates human activities. The nervous system undertakes to feel external stimuli, produce, process, transmit and integrate signals, carry out advanced cognitive activities, and engage in motor control and other important functions. It is a new research method rising in recent years to study the message processing and transmission mechanism of brain network nervous system combined with the related theory of complex network. Through this research method, we can better understand and understand the cognitive behavior of brain neural network. The research shows that the real brain neural system network has obvious small world network characteristics. With the deepening of the research, it is found that the real brain neural system network also has the characteristics of scale-free network. In this paper, according to the theory of complex network, the small world nervous system network model and scale-free nervous system network model are established. The nodes of the network are defined as neurons, the HH neuron model is used to describe the dynamic system state of the network nodes, and the synchronization of the two kinds of complex network models of brain nervous system is studied. First of all, the basic knowledge of nervous system dynamics and the basic theory of complex network are introduced. Several mathematical models of nervous system dynamics commonly used in nervous system dynamics are described in detail, and three main research directions of nervous system dynamics, namely random resonance, coherent resonance and synchronous dynamics of nervous system, are introduced. Secondly, according to the HH neuron model in the mathematical model of nervous system dynamics, the WS small-world nervous system network is constructed based on the complex network theory, and the synchronization of the network model is studied. The phase of the network node of the small world God system is defined by the analytical signal approximation method. The membrane voltage of the neuron is taken as the state variable of the system, and the phase synchronization state of the network is judged by calculating the average frequency of the network. The numerical simulation is carried out by matlab, and the simulation image is analyzed. It is concluded that the phase synchronization of small world neural network is closely related to the coupling degree and reconnection probability of the network. Then, combining the complex network theory with the HH neuron model in the mathematical model of nervous system dynamics, the BA scale-free neural network is constructed, and the synchronization of the network model is studied. The simulation results in matlab environment show that when the coupling strength exceeds the critical coupling strength, the synchronization phenomenon will occur in the network. In the process of constructing the scale-free nervous system network, the synchronization performance of the network is determined by the number of edges connected to the existing nodes with each neuron node added, and the larger the m, the better the synchronization performance of the network.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：R318

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