Local numerical analysis of Hopf bifurcation

This paper contributes to a local numerical analysis of Hopf bifurcation in the sense of a bordered systems approach. However, the method proposed enables us to decide about stability exchange between a stable steady-state and bifurcating orbit without explicit knowledge about the spectrum of the monodromy matrix. A kind of numerical Liapunov-Schmidt reduction is presented as a tool for continuation and Newton-like corrector of Hopf points. The proposed algorithm gives necessary data for local qualitative analysis of the Hopf bifurcation. The data enable us to determine degeneracy of the Hopf bifurcation and stability of bifurcating orbits and to predict periodic orbits. The equivariant form of the reduction and its application are discussed as well.