Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable
Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable
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DOI：
10.1088/1674-1056/19/8/080513
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发表时间：
2010-08
影响因子：
1.7
通讯作者：
莫娟;李玉叶;魏春玲;杨明浩;古华光;屈世显;任维
中科院分区：
文献类型：
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作者：
莫娟;李玉叶;魏春玲;杨明浩;古华光;屈世显;任维
为了进一步识别在生物实验和微分Chay模型模拟中观察到的加周期分岔场景的动力学，本文根据模拟结果拟合了Chay模型慢控制变量的不连续映射。在不连续映射中还再现了加周期级联中从周期k到周期k + 1爆发（k = 1，2，3，4）的加周期分岔过程以及每个分岔点附近噪声的随机效应.此外，边界碰撞分岔的动力学被确定在不连续映射，这是用来理解实验观察到的周期增量序列。简单的不连续映射在模拟神经群体的集体行为（如大型神经回路中的同步）方面具有重要的实际意义。
To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with the differential Chay model, this paper fits a discontinuous map of a slow control variable of the 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 are 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 the modeling of collective behaviours of neural populations like synchronization in large neural circuits.