SYMBOLIC COMPUTATION OF NORMAL FORMS FOR RESONANT DOUBLE HOPF BIFURCATIONS USING A PERTURBATION TECHNIQUE

摘要

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 coefficients 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.