  Based on the gauge potential decomposition theory and the $\phi $-mapping
theory, the topological inner structure of the Chern-Simons-Higgs vortex has
been showed in detail. The evolution of CSH vortices is studied from the
topological properties of the Higgs scalar field. The vortices are found
generating or annihilating at the limit points and encountering, splitting or
merging at the bifurcation points of the scalar field $\phi .$
