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

被引：0

作者：

莫娟 ^{[1
]}

李玉叶 ^{[1
]}

魏春玲 ^{[1
]}

杨明浩 ^{[1
]}

古华光 ^{[1
]}

屈世显 ^{[2
]}

任维 ^{[1
]}

机构：

[1] College of Life Science,Shaanxi Normal University

[2] College of Physics and Information Technology,Shaanxi Normal University

来源：

Chinese Physics B | 2010年 / 08期

基金：

中央高校基本科研业务费专项资金资助; 中国国家自然科学基金;

关键词：

period-adding bifurcation; border-collision bifurcation; discontinuous maps; neural bursting pattern;

D O I：

暂无

中图分类号：

O231 [控制论（控制论的数学理论）];

学科分类号：

070105 ; 0711 ; 071101 ; 0811 ; 081101 ;

摘要：

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.

引用

页码：225 / 240

页数：16