Bifurcation analysis of complex bursting induced by two different time-scale slow variables

Zhuoqin Yang; Tingting Guan

doi:10.3934/proc.2011.2011.1440

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2011, Volume 2011: 1440-1447. Doi: 10.3934/proc.2011.2011.1440 open access

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Bifurcation analysis of complex bursting induced by two different time-scale slow variables

Zhuoqin Yang^1, and
Tingting Guan²

1.
School of Mathematics and System Sciences, Beihang University, Beijing 100191
2.
School of Mathematics and System Sciences and LMIB, Beihang University, Beijing, 100191

Received: June 30, 2010

Revised: March 31, 2011

Published: August 2017

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Abstract

In Wierschem and Bertram model describing bursting modulated by slow glycolytic oscillation, different complex bursting patterns are produced by interaction of two slow variables with different time scales. Generation mechanisms of the complex bursting patterns with one or multiple short bursts and a long burst, are investigated by an extended fast/slow analysis, when a faster slow variable is considered as a bifurcation parameter of fast subsystem, while a slower slow variable only has an effect on bifurcation curves of the fast subsystem.

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Mathematics Subject Classification: Primary: 37G15, 74H60; Secondary: 92B20.

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