Bursting patterns and mixed-mode oscillations in reduced Purkinje model
Feibiao Zhan , Shenquan Liu, Jing Wang and Bo Lu
Bursting discharge is a ubiquitous behavior in neurons, and abundant bursting patterns imply many physiological information. There exists a closely potential link between
bifurcation phenomenon and the number of spikes per burst as well as mixed-mode oscillations (MMOs). In this paper, we have mainly explored the dynamical behav-ior of the reduced Purkinje cell and the existence of MMOs. First, we adopted the codimension-one bifurcation to illustrate the generation mechanism of bursting in the
reduced Purkinje cell model via slow{fast dynamics analysis and demonstrate the pro-cess of spike-adding. Furthermore, we have computed the rst Lyapunov coecient of
Hopf bifurcation to determine whether it is subcritical or supercritical and depicted the diagrams of inter-spike intervals (ISIs) to examine the chaos. Moreover, the bifurcation diagram near the cusp point is obtained by making the codimension-two bifurcation analysis for the fast subsystem. Finally, we have a discussion on mixed-mode oscillations and it is further investigated using the characteristic index that is Devils staircase.
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