  Using semi-analytic models of galaxy formation, we investigate the properties
of $z\sim3$ galaxies and compare them with the observed population of
Lyman-break galaxies (LBGs). In addition to the usual quiescent mode of star
formation, we introduce a physical model for starbursts triggered by
galaxy-galaxy interactions. We find that with the merger rate that arises
naturally in the CDM-based merging hierarchy, a significant fraction of bright
galaxies identified at high redshift ($z \ga 2$) are likely to be low-mass,
bursting satellite galaxies. The abundance of LBGs as a function of redshift
and the luminosity function of LBGs both appear to be in better agreement with
the data when the starburst mode is included, especially when effects of dust
extinction are considered. The objects that we identify as LBGs have observable
properties including low velocity dispersions that are in good agreement with
the available data. In this ``Bursting Satellite'' scenario, quiescent star
formation at $z\ga2$ is relatively inefficient and most of the observed LBGs
are starbursts triggered by satellite mergers within massive halos. In
high-resolution N-body simulations, we find that the most massive dark matter
halos cluster at redshift $z\sim 3$ much as the LBGs are observed to do. This
is true for both the $\Omega=1$ CHDM model and low-$\Omega$ \LCDM and OCDM
models, all of which have fluctuation power spectra $P(k)$ consistent with the
distribution of low-redshift galaxies. The Bursting Satellite scenario can
resolve the apparent paradox of LBGs that cluster like massive dark matter
halos but have narrow linewidths and small stellar masses.
