Dynamical Characteristics of a Hodgkin-Huxley neuron
  By means of the concepts of factorial moment, return map and NM estimator, we analyze some responses of a HH neuron to various types of spike-train inputs. The corresponding fractal dimensions and values of NM estimators can describe the correlation characteristics quantitatively. It is found that all the intervals of successive output spikes may obey a power-law for some conditions. And in time scale the output series for a HH model for each type of inputs is correlated with typical correlation length and correlation strength. These power-law and correlation characteristics may be useful in the coding and decoding process of HH neurons. These concepts may distinguish different inputs quantitatively.   PACS number(s): 87.18.Sn, 84.35.+i, 05.45.Tp 
Huijie Yang, Fangcui Zhao, Yizhong Zhuo, Xizhen Wu, Zhuxia Li