  Within the framework of the improved isospin dependent quantum molecular
dynamics (ImIQMD) model, the dynamics of strangeness (K$^{0,+}$, $\Lambda$ and
$\Sigma^{-,0,+}$) production in heavy-ion collisions near threshold energies is
investigated systematically, in which the strange particles are considered to
be mainly produced by the inelastic collisions of baryon-baryon and
pion-baryon. The collisions in the region of supra-saturation densities of the
dense baryonic matter formed in heavy-ion collisions dominate the yields of
strangeness production. The total multiplicities as functions of incident
energies and collision centralities are calculated with the Skyrme parameter
SLy6. The excitation function of strangeness production is analyzed and also
compared with the KaoS data for the K$^{+}$ production in the reactions
$^{12}$C+$^{12}$C and $^{197}$Au+$^{197}$Au.
