Calculation of High-Order Normal Form of Multi-Dimensional Nonlinear Dynamical System

Calculating normal form is one of the main methods on studying nonlinear dynamical system. Finding the general normal form is one of the two main parts in the calculating. There are matrix-expressing, conjugate-operator and Lie-algebra methods, which can be used. The matrix-expressing method is suitable for being mechanized. In this paper, a Mathematica package is presented for calculating normal form with matrix-expressing method combined symmetric theory. With the symbolic deduction, the package possesses generality in calculating the general normal form of semi-simple case and non-semi-simple case. It can be used for calculating high order normal form of multi-dimensional dynamical systems.