Recent photometric observations by the {\it Hubble Space Telescope (HST)}
have revealed the physical properties of stellar galactic nuclei in nucleated
dwarf galaxies in the Virgo cluster of galaxies. In order to elucidate the
formation processes of nucleated dwarfs, we numerically investigate gas
dynamics, star formation, and chemical evolution within the central 1 kpc of
gas disks embedded within the galactic stellar components of non-nucleated
dwarfs. We find that high density, compact stellar systems can be formed in the
central regions of dwarfs as a result of dissipative, repeated merging of
massive stellar and gaseous clumps developed from nuclear gaseous spiral arms
as a result of local gravitational instability. The central stellar components
are found to have stellar masses which are typically  5% of their host dwarfs
and show very flattened shapes, rotational kinematics, and central velocity
dispersions significantly smaller than those of their host dwarfs. We also find
that more massive dwarfs can develop more massive, more metal-rich, and higher
density stellar systems in their central regions, because star formation and
chemical enrichment proceed more efficiently owing to the less dramatic
suppression of star formation by supernovae feedback effects in more massive
dwarfs. Based on these results, we suggest that gas-rich, non-nucleated dwarfs
can be transformed into nucleated ones as a result of dissipative gas dynamics
in their central regions. We discuss the origin of the observed correlations
between physical properties of stellar galactic nuclei and those of their host
galaxies.Comment: 13 pages, 4 figures (1 color), ApJL in pres