English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

On decomposing mixed-mode oscillations and their return maps

MPS-Authors
/persons/resource/persons184683

Kuehn,  C.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

Locator
There are no locators available
Fulltext (public)
There are no public fulltexts available
Supplementary Material (public)
There is no public supplementary material available
Citation

Kuehn, C. (2011). On decomposing mixed-mode oscillations and their return maps. Chaos, 21(3): 033107.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-8C33-3
Abstract
Alternating patterns of small and large amplitude oscillations occur in a wide variety of physical, chemical, biological, and engineering systems. These mixed-mode oscillations (MMOs) are often found in systems with multiple time scales. Previous differential equation modeling and analysis of MMOs have mainly focused on local mechanisms to explain the small oscillations. Numerical continuation studies reported different MMO patterns based on parameter variation. This paper aims at improving the link between local analysis and numerical simulation. Our starting point is a numerical study of a singular return map for the Koper model which is a prototypical example for MMOs, which also relates to local normal form theory. We demonstrate that many MMO patterns can be understood geometrically by approximating the singular maps with affine and quadratic maps. Motivated by our numerical analysis we use abstract affine and quadratic return map models in combination with two local normal forms that generate small oscillations. Using this decomposition approach we can reproduce many classical MMO patterns and effectively decouple bifurcation parameters for local and global parts of the flow. The overall strategy we employ provides an alternative technique for understanding MMOs. (C) 2011 American Institute of Physics. [doi:10.1063/1.3615231]