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

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.

Keywords: period-adding bifurcation border-collision bifurcation discontinuous maps neural bursting pattern

Received: 30 December 2009
Revised: 24 January 2010
Accepted manuscript online:

PACS:	87.19.L-	(Neuroscience)
	87.19.R-	(Mechanical and electrical properties of tissues and organs)

Fund: 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).

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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 2010 Chin. Phys. B 19 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

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