  The topological structure of the electric topological current of the locally
gauge invariant Maxwell-Chern-Simons Model and its bifurcation is studied. The
electric topological charge is quantized in term of winding number. The Hopf
indices and Brouwer degree labeled the local topological structure of the
electric topological current. Using $\Phi $-mapping method and implicity
theory, the electric topological current is found generating or annihilating at
the limit points and splitting or merging at the bifurcate points. The total
electric charge holds invariant during the evolution.
