Abstract

In this chapter, by researching the algorithm of the formal series, and deducing the recursion formula of computing the nondegenerate and degenerate singular point quantities on center manifold, we investigate the Hopf bifurcation of high-dimensional nonlinear dynamic systems. And more as applications, the singular point quantities for two classes of typical three- or four-dimensional polynomial systems are obtained, the corresponding multiple limit cycles or Hopf cyclicity restricted to the center manifold are discussed.

Keywords: high-dimensional system, center manifold, Hopf bifurcation, singular point quantities
