  The lattice Hamiltonian with the presence of a chiral magnetic isotropic
Dzyaloshinskii-Moriya interaction (DMI) in a square and hexagonal lattice is
numerically solved to give the full phase diagram consisting of skyrmions and
merons in different parameter planes. The phase diagram provides the actual
regions of analytically unresolved asymmetric skyrmions and merons, and it is
found that these regions are substantially larger than those of symmetric
skyrmions and merons. With magnetic field, a change from meron or spin spiral
to skyrmion is seen. The complete phase diagram for the $C_{nv}$ symmetric
system with anisotropic DMI is drawn and it is shown that this DMI helps to
change the spin spiral propagation direction. Finally, the well-defined region
of a thermodynamically stable antiskyrmion phase in the $C_{nv}$ symmetric
system is shown.
