Bursting types and bifurcation analysis of the temperature-sensitive Purkinje neuron

The bursting discharge behaviour of neurons is affected by many factors, among which temperature is one of the more important factors. In this work, we study the bursting discharge behaviour and dynamics process of two different temperature-sensitive ion channels, the temperature-sensitive potassium current and the temperature-sensitive calcium current. In the case of the temperature-sensitive potassium current, the bursting discharge waveforms, codimension-1 bifurcations and trajectory plots at different temperatures indicate that five different types of bursting discharge (Hopf/Flip, Hopf/Homoclinic, Fold/Homoclinic, Fold/Fold Cycle, Circle/Big Homoclinic) appear with increasing temperature. In the case of temperature-sensitive calcium current, two types of bursting discharge (Circle/Big Homoclinic, Fold/Fold Cycle) emerge. According to the bursting discharge waveforms, the rise in temperature can promote the generation of bursting discharge at the beginning, and finally, the bursting discharge phenomenon disappears. This is consistent with the experimental results that blocking potassium and calcium currents can promote the bursting of Purkinje neurons. Then, it can be seen from the codimension-2 bifurcation and the waveform area distribution diagrams that even if the dynamic paths are consistent, the bursting discharge types and the waveforms may be different. In contrast, even if the bursting discharge type is the same, the dynamic paths and the waveform may be different. These results provide insight into the effect of temperature on the neuronal dynamics and bursting behaviour of temperature-sensitive ion channels.