  Scaling relations of metallicity (O/H), star formation rate (SFR), and
stellar mass give important insight on galaxy evolution. They are obeyed by
most galaxies in the Local Universe and also at high redshift. In a companion
paper, we compiled a sample of ~1100 galaxies from redshift 0 to ~3, spanning
almost two orders of magnitude in metal abundance, a factor of $\sim10^6$ in
SFR, and of ~10^5 in stellar mass. We have characterized empirically the
star-formation "main sequence" (SFMS) and the mass-metallicity relation (MZR)
for this sample, and also identified a class of low-metallicity starbursts,
rare locally but more common in the distant universe. These galaxies deviate
significantly from the main scaling relations, with high SFR and low metal
content for a given M*. In this paper, we model the scaling relations and
explain these deviations from them with a set of multi-phase chemical evolution
models based on the idea that, independently of redshift, initial physical
conditions in a galaxy's evolutionary history can dictate its location in the
scaling relations. Our models are able to successfully reproduce the O/H, M*,
and SFR scaling relations up to z~3, and also successfully predict the
molecular cloud fraction as a function of stellar mass. These results suggest
that the scaling relations are defined by different modes of star formation: an
"active" starburst mode, more common at high redshift, and a quiescent
"passive" mode that is predominant locally and governs the main trends.
