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2015 | OriginalPaper | Chapter

11. Computing Manifolds

Author : Christian Kuehn

Published in: Multiple Time Scale Dynamics

Publisher: Springer International Publishing

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Abstract

We have extensively discussed the properties of invariant manifolds and their relevance for fast–slow systems in previous chapters. However, we usually used explicit algebraic expressions or asymptotic expansions to deal with critical and slow manifolds. For a general multiple time scale system, there are several complications. They may not be in standard form, and even if they are, then calculating a slow manifold analytically may be intractable. This chapter deals with algorithms to find and compute invariant manifolds for fast–slow systems numerically.

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previous chapter Numerical Methods
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Metadata
Title
Computing Manifolds
Author
Christian Kuehn
Copyright Year
2015
Book
Multiple Time Scale Dynamics

Print ISBN: 978-3-319-12315-8

Electronic ISBN: 978-3-319-12316-5

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-12316-5_11

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