✦ LIBER ✦

A RECURSIVE APPROACH TO COMPUTE NORMAL FORMS

✍ Scribed by L. HSU; L.J. MIN; L. FAVRETTO

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 388 KB
Volume: 243
Category: Article
ISSN: 0022-460X
DOI: 10.1006/jsvi.2000.3422

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✦ Synopsis

Normal forms are instrumental in the analysis of dynamical systems described by ordinary di!erential equations, particularly when singularities close to a bifurcation are to be characterized. However, the computation of a normal form up to an arbitrary order is numerically hard. This paper focuses on the computer programming of some recursive formulas developed earlier to compute higher order normal forms. A computer program to reduce the system to its normal form on a center manifold is developed using the Maple symbolic language. However, it should be stressed that the program relies essentially on recursive numerical computations, while symbolic calculations are used only for minor tasks. Some strategies are proposed to save computation time. Examples are presented to illustrate the application of the program to obtain high order normalization or to handle systems with large dimension.

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