 found that the SC order parameter with $s_{\pm}=\Delta_{0}\cos(k_{x})\cos(k_{y})$ symmetry is the most favorable pairing at both the electron- and hole-doped sides, while the LDOS exhibits the characteristic of nodal gap for the former and full gap for the latter. In the vortex states, the emergence of the field-induced SDW order depends heavily on the strength of the Hund's coupling and the Coulomb repulsions. The coexistence of the field-induced SDW order and SC order around the core region is realized due to the fact that the two orders emerge at different energies. The 