Symbolic software development for computing the normal form of double Hopf bifurcation

A method is presented for computing the normal form of double Hopf bifurcation associated with non-semi-simple 1:1 resonance. The method combines the normal form theory and the center manifold theory to deal with a general n-dimensional system. Explicit recursive formulas are derived for the coefficients of the normal form and the associated nonlinear transformations. User-friendly computer software is developed using a symbolic computation language Maple. This enables one to easily compute the normal form and nonlinear transformation for a given specific problem up to an arbitrary order. An illustrative example is given to show the applicability of the method and the convenience of the software.