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. © 2006 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Borok, S., Goldfarb, I., Gol’Dshtein, V., & Maas, U. (2006). Ghost ILDM-manifolds and their identification. In Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena (pp. 55–79). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-35888-9_4
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