NORMAL FORM AND CODIMENSION 3 DEGENERATE BIFURCATION OF A NONLINEAR DYNAMICAL SYSTEM

In this paper we use matrix representation method to compute the higher order normal form of a nonlinear dynamical system with Z2-symmetry. We obtain universal unfoldings corresponding to normal forms for codimension 2 and codimension 3 degenerate cases. Finally we use obtained normal form and universal unfolding to discuss codimension 3 degenerate bifurcations of nonlinear dynamical system.