Computation of the Unique Normal Form for Nonlinear Dynamical Systems in the Mechanical Applications

Abstract

Abstract. In the mechanical applications, research for degenerate bifurcations is usually connected with the normal form theory of nonlinear dynamical systems. In this paper, we mainly concern with the unique normal form for a class of three dimensional vector fields by the method of transformation with parameters. With the aid of the Maple software, a recursive formula for computing the coefficients of the normal form is given. Our results can be easily applied to investigate the direct bifurcation and stability of any model which can be written in this.