Ghost ILDM-manifolds and their identification

S. Borok, I. Goldfarb, V. Gol'Dshtein, U. Maas

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

3 Scopus citations


One of the popular methods (Intrinsic Low-Dimensional Manifolds - ILDM)) of decomposition of multiscale systems into fast and slow sub-systems for reduction of their complexity is considered in the present paper. The method successfully locates a position of slow manifolds of considered system and as any other numerical approach has its own disadvantages. In particular, an application of the ILDM-method produces so-called ghost-manifolds that do not have any connection to the true dynamics of the system. It is shown analytically that for two-dimensional singularly perturbed system (for which the fast-slow decomposition has been already done in analytical way) the ghost-manifolds appear. The problem of discrimination/identification of the ghost-manifolds is under consideration and two numerical criteria for their identification are proposed. A number of analyzed examples demonstrate efficiency of the suggested approach.

Original languageEnglish
Title of host publicationModel Reduction and Coarse-Graining Approaches for Multiscale Phenomena
PublisherSpringer Berlin Heidelberg
Number of pages25
ISBN (Print)3540358854, 9783540358855
StatePublished - 1 Dec 2006

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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