Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable

• Published in: Chinese physics B Vol. 19; no. 8; pp. 225 - 240
• Main Author: 莫娟 李玉叶 魏春玲 杨明浩 古华光 屈世显 任维
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.08.2010
• Subjects: 分岔点; 分歧; 控制变量; 爆破; 破译; 神经回路; 边界碰撞分岔; 连续映射
• ISSN: 1674-1056; 2058-3834
• DOI: 10.1088/1674-1056/19/8/080513

To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with differential Chay model, this paper fits a discontinuous map of a slow control variable of Chay model based on simulation results. The procedure of period adding bifurcation scenario from period k to period k ＋ 1 bursting （k = 1, 2, 3, 4） involved in the period-adding cascades and the stochastic effect of noise near each bifurcation point is also reproduced in the discontinuous map. Moreover, dynamics of the border-collision bifurcation is identified in the discontinuous map, which is employed to understand the experimentally observed period increment sequence. The simple discontinuous map is of practical importance in modeling of collective behaviours of neural populations like synchronization in large neural circuits.