A method for characterizing and identifying firing patterns of neural spike trains is presented. Based on the time evolution of a neural spike train, the counting process is constructed as a time-dependent stair-like function. Three characteristic variables defined at sequential moments, including two formal derivatives and the integration of the counting process, are introduced to reflect the temporal patterns of a spiketrain. The reconstruction of a spike train with these variables verify the validity of this method. And a model of cold receptor is used as an example to investigate the temporal patterns under different temperature conditions. The most important contribution of our method is that it not only can reflect the features of spike train patterns clearly by using the irgeometrical properties,but also it can reflect the trait of time, especially the change of bursting of spike train. So it is a useful complementarity to conventional method of averaging.
Du, Y., Lu , Q-S., Wang, S., & Wiercigroch, M. (2009). A new method for characterizing patters of neural spike trains and its application. International Journal of Non-Linear Mechanics, 44(4), 432–440. https://doi.org/10.1016/j.ijnonlinmec.2009.01.007