Computation of the Normal Form for 1:1 Resonant Double Hopf Bifurcation
نویسنده
چکیده
An efficient method is presented for computing the normal form of general n-dimensional systems associated with 1:1 resonant double Hopf bifurcation. The approach combines the computations of center manifold and normal form in one unified procedure. The Jacobian of the system evaluated at an equilibrium contains non-semisimple eigenvalues. Explicit formulas are obtained for directly computing the normal form and associated nonlinear transformation. An recursive approach is developed to reduce algebraic manipulations to the minimum at each order, which greatly saves computational time and computer memory. Symbolic programs using Maple have been implemented and applied to two illustrative examples.
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