Dynamic behavior of nonlinear systems at critical point of Hopf bifurcation

Abstract

This paper is concerned with the bifurcations of nonsemi-simple eigenvalues at critical piont of Hopf bifurcation to understand the dynamic behavior of the system around the critical point clearly. By using the Puiseux expansion, the expression of the bifurcation of non-semi-simple eigenvalues and the corresponding topological structure in the parameter space are obtained. The zero-order approximate solutions in the vicinity of the critical points at which the multiple Hopf bifurcation may occur are developed. A numerical example, the flutter problem of an airfoil in simplified model, is given to illustrate the application of the proposed method.