Symbolic Computation of Normal Forms for Resonant Double Hopf Bifurcations Using a Perturbation Technique
نویسنده
چکیده
This paper presents a perturbation method for computing the normal forms of resonant double Hopf bifurcations with the aid of a computer algebraic system. This technique, based on the method of multiple time scales, can be used to deal with general n-dimensional systems without the application of center manifold theory. Explicit iterative formulas have been derived for uniquely determining the coe$cients of normal forms and associated non-linear transformations up to an arbitrary order. User-friendly symbolic computer programs written in Maple have been developed, which can be easily applied for computing the normal forms of a given system. Examples are presented to show the applicability of the methodology and the convenience of using the computer software. ( 2001 Academic Press
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