Simplest Normal Forms of Generalized High Codimension Hopf Bifurcations
DING Yu-mei1 , ZHANG Qi-chang2
1.Tianjin University of Science and Technology, Tianjin 300222 , P. R. China;2.School of Mechanical Engineering, Tianjin University, Tianjin 300072, P. R. China
Abstract：The normal forms of generalized Hopf bifurcations have been extensively studied using normal form theory and the matrix representation method of dynamic system. In this paper, two theorems are presented to show that the conventional Hopf bifurcations can be further simplified. We calculate the simplest normal forms of generalized Hopf bifurcations with the following condition , but . Based on the conventional normal form, the generalized Hopf bifurcation system is further simplified to the simplest normal form there are at most two terms remaining in the amplitude equation of the simplest normal forms up to any order. There are two kinds of the simplest normal forms. Three algebra expression formulas are given.
2012, Vol. 31 
