Hodgkin-Huxley神经元体系分岔特性的理论研究

Theoretical Research on Bifurcation Characteristics of Hodgkin-Huxley Neuron System

摘要: 本文采用Hodgkin-Huxley (HH)神经元耦合系统为研究对象，通过计算机仿真模拟探讨体系内外环境中的噪声、耦合强度及系统尺度等因素对神经细胞分岔特性的影响。研究发现，一方面，在确定系统尺度和耦合强度的耦合体系中，增加噪声强度能够使神经元的分岔临界电流值降低，这表明适当的噪声有利于提高神经系统对外部微弱信号的响应能力。另一方面，耦合强度的增加会使得分岔点相应增大，而耦合单元数的增加则会使分岔点有所降低，表明合适的系统尺度和耦合强度有利于信息的传递。对分岔特性的深入了解，有助于理解这些因素对体系动力学行为调控作用规律和内在机理。其成果将为了解大脑神经网络的复杂功能以及与病理状态之间的关系提供新的启示。

Abstract: In this paper, by using the coupling Hodgkin-Huxley (HH) neural model, the bifurcation characte-ristic of neurons affected by noise, coupling strength, as well as system scale, is studied by com-puter simulation. It is found that, on the one hand, in the coupling system with certain scale and coupling strength, the bifurcation current of neurons may decrease with the increasing strength of noise, and this indicates that the appropriate noise can improve the response ability to the external weak signal. On the other hand, the bifurcation point will increase with the coupling strength, while will reduce with the increase of the number of coupling units. These indicate that the appropriate system scale and coupling strength are beneficial to the transmission of information. A better understanding of bifurcation characteristics is helpful to understand the regulation and internal mechanism of these factors on the dynamics of the system. The results will provide new insights for understanding the complex functions of the brain neural network and the relationship between the pathology and the state of the brain.