两房室神经元模型的同步簇放电的动力学分析

DYNAMICS ANALYSIS OF SYNCHRONOUS BURSTING IN TWO-COMPARTMENT NEURON MODEL

研究一个具有电流反馈的两房室锥体神经元的簇放电动力学问题.首先,利用数值模拟研究了该神经元的树突和胞体两个房室之间的峰相位同步行为.其次,基于快慢动力学分析方法,给出了快子系统的双参数分岔曲线图,结果表明快子系统产生了3个余维-2分岔点,它们分别为fold-Hopf分岔点ZH、Cusp分岔点CP和Bogdanov-Takens分岔点BT.最后,根据这些余维-2分岔点确定系统存在着丰富的簇放电模式,如"fold/fold"型,"Hopf/Hopf"型,"Hopf/homoclinic"型以"fold/homoclinic"型簇振荡等,并分析研究了簇放电模式的产生以及它们之间相互转迁的动力学机理.本文的研究结果进一步表明了神经元的几何形态特性对于神经元放电模式多样性的重要影响.

A two-compartment neuron model with outside current feedback is considered in order to study the dynamics of bursting patterns. Firstly, on the base of numerical simulation, the behavior of phase synchronization for the spikes in the soma and dendrite compartments is investigated. Secondly, by using fast-slow dynamics analysis, two-parameter bifurcation analysis of the fast subsystem is performed in the two-parameter plane. It is shown that three condimension-2 bifurcation points are generated in the fast subsystem, i. e. , fold-Hopf bifurcation ZH, cusp bifurcation CP and Bogdanov-Takens bifurcation BT. Finally, these condimension-2 bifurcation points determine that different bursting oscillations occurs in the system, such as ＂fold/fold＂ type, ＂Hopf/Hopf＂ type, ＂Hopf/homoclinic＂ type and ＂fold/homoclinic＂ type. Furthermore, the generation and transition mechanisms of different bursting patterns are discussed. The results offer significant data for understanding the important role of the geometric parameter in the variety of neuronal firing activities