ABSTRACT
This chapter describes some of the techniques used to calculate normal forms. It deals with applications of the Hopf bifurcation and presents an example of codimension two bifurcations. The chapter discusses the theory of normal forms, which uses a coordinate transformation to reduce the system to a simpler form containing all the dynamics. It considers applications of the normal forms theory and the Hopf bifurcation and the bifurcation of the Rossler system. A normal form is the simplest representation of a class of equations featuring a specific bifurcation phenomenon. The normal form is sufficient information to understand the dynamical behavior in the neighborhood of a bifurcation. The chapter examines the procedure used to find the normal form of a system of differential equations through the eigenvalues of the Jacobian matrix.
