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

doi:10.1088/1674-1056/19/8/080513

中国物理B ›› 2010, Vol. 19 ›› Issue (8): 80513-080513.doi: 10.1088/1674-1056/19/8/080513

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

莫娟¹, 李玉叶¹, 魏春玲¹, 杨明浩¹, 古华光¹, 任维¹, 屈世显²

(1)College of Life Science, Shaanxi Normal University, Xi'an 710062, China; (2)College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China

收稿日期:2009-12-30 修回日期:2010-01-24 出版日期:2010-08-15 发布日期:2010-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10774088, 10772101, 30770701 and 10875076) and the Fundamental Research Funds for the Central Universities (Grant No. GK200902025).

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

Mo Juan(莫娟)^a), Li Yu-Ye(李玉叶)^a), Wei Chun-Ling(魏春玲)^a), Yang Ming-Hao(杨明浩)^a), Gu Hua-Guang(古华光)^a)†ger, Qu Shi-Xian(屈世显)^b), and Ren Wei(任维)^a)

^a College of Life Science, Shaanxi Normal University, Xi'an 710062, China; ^b College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China

Received:2009-12-30 Revised:2010-01-24 Online:2010-08-15 Published:2010-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10774088, 10772101, 30770701 and 10875076) and the Fundamental Research Funds for the Central Universities (Grant No. GK200902025).

摘要/Abstract

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.

Abstract: 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.

Key words: period-adding bifurcation, border-collision bifurcation, discontinuous maps, neural bursting pattern

中图分类号: (Neuroscience)

87.19.L-

87.19.R- (Mechanical and electrical properties of tissues and organs)

莫娟, 李玉叶, 魏春玲, 杨明浩, 古华光, 屈世显, 任维. Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable[J]. 中国物理B, 2010, 19(8): 80513-080513.

Mo Juan(莫娟), Li Yu-Ye(李玉叶), Wei Chun-Ling(魏春玲), Yang Ming-Hao(杨明浩), Gu Hua-Guang(古华光), Qu Shi-Xian(屈世显), and Ren Wei(任维). Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable[J]. Chin. Phys. B, 2010, 19(8): 80513-080513.

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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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