两类Morris-Lecar模型的动力学分析

发布时间：2018-05-14 07:17

本文选题：Morris-Lecar模型 + 簇放电　；参考：《华南理工大学》2015年硕士论文

【摘要】：随着计算神经科学的不断发展与完善,各类神经元模型的放电模式及分支理论已经被广泛研究,如Hodgkin-Huxley模型、Morris-Lecar模型、Hindmarsh-Rose模型等,为我们更加深入的学习和研究神经系统的信息编码和认知功能奠定了基础.本文主要研究改进的Morris-Lecar模型及建立在脊髓第I层神经元上的一类Morris-Lecar-like模型的动力学性质,得到的主要结果如下:对于改进的Morris-Lecar模型,我们首先通过数值模拟研究生理参数膜电容对神经元膜电位发放序列的影响,得到丰富的神经元放电模式.然后结合峰峰间期序列ISIs分岔图我们发现,当膜电容对应不同的值时,一定范围内时间尺度因子和钙离子最大电导的变化所引起的神经元的放电模式有很大的区别,如峰发放、簇发放或不规则发放,并且在这些发放模式之间的转移中我们也发现了几种典型的非线性动力学现象,包括倍周期分岔、加周期分岔等现象,使我们进一步理解了神经元的信息编码与膜电容、离子通道等共同作用之间的关系.文章最后研究Morris-Lecar-like模型,我们首先对双参数分支图中的Bogdanov-Takens点附近的分支情况进行数值计算,得到相应的鞍-结点分支曲线、Hopf分支曲线和同宿轨分支曲线;同时为了使神经元产生更丰富的放电现象,我们引进慢变量,根据快子系统的平衡点曲线上支的Hopf分支点数量的不同,我们对得到的五种簇放电模式的动力学性质进行了研究.
[Abstract]:With the development and perfection of computational neuroscience, the discharge modes and branching theories of various neuronal models, such as the Hodgkin-Huxley model, the Morris-Lecar model and Hindmarsh-Rose model, have been extensively studied. It lays a foundation for us to further study the information coding and cognitive function of the nervous system. In this paper, the dynamic properties of the improved Morris-Lecar model and a class of Morris-Lecar-like model based on the spinal layer I neurons are studied. The main results are as follows: for the improved Morris-Lecar model, Firstly, the effects of membrane capacitance on the release sequence of membrane potential of neurons were studied by numerical simulation, and a rich pattern of neuronal discharge was obtained. Then combining with the ISIs bifurcation diagram of the interpeak series, we find that when the membrane capacitance corresponds to different values, the firing patterns of neurons caused by the change of the time scale factor and the maximum conductance of calcium ion in a certain range are quite different, such as peak discharge. Cluster distribution or irregular distribution, and in the transfer between these modes, we also find several typical nonlinear dynamic phenomena, including double period bifurcation, plus period bifurcation and so on. We can further understand the relationship between the information coding of neurons and the interaction of membrane capacitance and ion channel. Finally, we study the Morris-Lecar-like model. Firstly, we numerically calculate the bifurcation near the Bogdanov-Takens point in the two-parameter bifurcation graph, and obtain the corresponding saddle-node bifurcation curve and homoclinic orbit bifurcation curve. At the same time, in order to make neurons produce more abundant discharge phenomena, we introduce slow variables. According to the number of Hopf branch points on the equilibrium point curve of fast subsystem, we study the dynamic properties of the five cluster discharge modes.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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