purkinje cell dendrite
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Author(s):  
Xiaoshan Huang ◽  
Shenquan Liu ◽  
Pan Meng ◽  
Jie Zang

This paper mainly studied firing patterns and related bifurcations in the Purkinje cell dendrite model. Based on the methods of equivalent potentials and time scale analysis, the initial six-dimensional (6D) dendrite model is reduced to a 3D form to facilitate the calculation. We numerically show that the dendrite model could exhibit period-adding bifurcation and four bursting patterns for several vital parameters. Then the bifurcation mechanisms and transition of these four bursting patterns are discussed by phase plane analysis, and two-parameter bifurcation analysis of the fast subsystem, respectively. Moreover, we computed the first Lyapunov coefficient to determine the stability of Hopf bifurcation. Ultimately, we analyzed the codimension-two bifurcation of the whole system and gave a detailed theoretical derivation of the Bogdanov–Takens bifurcation.


2010 ◽  
Vol 35 (12) ◽  
pp. 2135-2143 ◽  
Author(s):  
Simona D’Antoni ◽  
Laura Zambusi ◽  
Franca Codazzi ◽  
Daniele Zacchetti ◽  
Fabio Grohovaz ◽  
...  

2008 ◽  
Vol 105 (11) ◽  
pp. 4483-4488 ◽  
Author(s):  
S. Donald ◽  
T. Humby ◽  
I. Fyfe ◽  
A. Segonds-Pichon ◽  
S. A. Walker ◽  
...  

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