Top panels: HOD measured for galaxies with M_r − 5log₁₀(h) <  − 17 at redshifts z = 0, z = 0.3, and z = 0.5 for the MDPL2-SAG simulation. The blue lines represents the HOD of the complete catalogs, while the black and red lines show the HOD of halos inside the cosmic voids identified in each snapshot. Bottom panels: Ratio of the HOD inside voids to the HOD in the complete catalogs at each redshift. The error bars were estimated via the Jackknife resampling method and using 50 subsamples.