HH模型阈值特性分析及参数空间拟合

Analysis of threshold characteristics of HH model and parameter fitting.

通过寻求HH(Hodgkin-Huxley)模型中参数的变化与阈值变化之间的关系,得到神经元的阈值特性.首先,根据神经元阈下离子通道的特性来对四维HH模型做一定的简化,使所得到的二维简化模型保持原有四维HH模型的阈值特性.然后,用相平面法来对简化模型的阈值特性进行定性分析,给出了参数变化与二维简化模型中的鞍点电压值变化之间的关系.最后,把四维HH模型的数值仿真结果与相平面分析结果进行对照,发现可用鞍点附近动力学特性来反映阈值特性.在定性上,这是一种寻求参数变化与阈值变化关系的方法,也是分析阈值下参数空间的手段.

The HH (Hodgkin-Huxley) model, based on the neuropsychological characteristics, was used to analyze the threshold behavior of realistic neuron axon and the relationship of changes of the parameter and the threshold. Firstly, the two-dimensional simplified model which hold the characteristics of four-dimensional HH model was obtained. Secondly, the phase planes were introduced to find qualitatively the threshold of dynamical behavior, and the influences of parameters change on saddle point were discussed. Finally, by numerical simulation it was showed that the dynamical characteristics near the saddle point reflects the threshold behavior of four-dimensional HH model. So, a new method is attained to seek the sub-threshold parameter space.