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  Sub-Hopf/fold-cycle bursting and its relation to (quasi-)periodic oscillations

Straube, R., Flockerzi, D., & Hauser, M. J. B. (2006). Sub-Hopf/fold-cycle bursting and its relation to (quasi-)periodic oscillations. Journal of Physics: Conference Series, 55, 214-231. doi:10.1088/1742-6596/55/1/020.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-9B32-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0027-BDC4-7
Genre: Journal Article

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 Creators:
Straube, R.1, Author              
Flockerzi, D.2, Author              
Hauser, M. J. B.3, Author
Affiliations:
1Systems Biology, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society, ou_1738155              
2Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society, ou_1738154              
3Otto-von-Guericke University Magdeburg, ou_persistent22              

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 Abstract: We investigate the emergence of bursting oscillations and its relation to (quasi-) periodic behaviour in two different model systems, a pH oscillator and a calcium oscillator. Both systems are described by 3-dimensional ODE systems and follow different `routes' to bursting oscillations as parameters are varied. In the first part, we exploit the slow-fast structure of the 3-dimensional ODE systems to show that the bursting oscillations are of sub-Hopf/fold-cycle type over a wide range of parameters. For this purpose, a slow variable is used as a quasi-static bifurcation parameter for the remaining 2-dimensional fast subsystem. For the pH oscillator, a subsequent two-parameter continuation reveals a transition in the bursting behaviour from sub-Hopf/fold-cycle to fold/sub-Hopf type. In the second part, we argue that the particular constellation of a subcritical Hopf bifurcation together with a saddle-node bifurcation of a periodic orbit (fold-cycle) may not only account for the bursting oscillations, but also allows for (quasi-)periodic oscillations on a 2-torus suggesting a common origin for both types of dynamics. © 2013 IOP Publishing [accessed 2013 June 13th]

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Language(s): eng - English
 Dates: 2006
 Publication Status: Published in print
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 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1088/1742-6596/55/1/020
eDoc: 298316
Other: 46/06
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Title: Journal of Physics : Conference Series
Source Genre: Journal
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Pages: - Volume / Issue: 55 Sequence Number: - Start / End Page: 214 - 231 Identifier: ISSN: 1742-6588