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

作　　者：莫娟 李玉叶 魏春玲 杨明浩 古华光 屈世显 任维 

机构地区：[1]College of Life Science,Shaanxi Normal University [2]College of Physics and Information Technology,Shaanxi Normal University

出　　处：《Chinese Physics B》2010年第8期225-240,共16页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.10774088,10772101,30770701 and 10875076);the Fundamental Research Funds for the Central Universities(Grant No.GK200902025)

摘　　要：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.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.

关 键 词：period-adding bifurcation border-collision bifurcation discontinuous maps neural bursting pattern 

分 类 号：O231[理学—运筹学与控制论]