  We compute chemical evolution models to constrain the mode and the history of
star formation in starburst galaxies as a whole, i.e. over a large range of
mass and metallicity. To this end, we investigate the origin of the dispersion
observed in the evolution of both nitrogen-to-oxygen abundance ratio and galaxy
luminosity as a function of metallicity for a large sample of starburst
galaxies. We find that the variation of the star formation efficiency, in the
framework of continuous star formation models, produce a scatter equivalent to
what is observed in the N/O versus O/H diagram for low-mass HII galaxies only.
However, continous star formation models are unable to reproduce i) the scatter
observed for massive starburst and UV-selected galaxies in the N/O versus O/H
relation, and ii) the scatter in the luminosity versus O/H scaling relation
observed for the whole sample of starburst galaxies. The dispersion associated
with the distribution of N/O as a function of metallicity, for both low-mass
and massive galaxies, is well explained in the framework of bursting star
formation models. It is interpreted as a consequence of the time-delay between
the ejection of nitrogen and that of oxygen into the ISM. These models also
reproduce the spread observed in the luminosity-metallicity relation.
Metal-rich spiral galaxies differ from metal-poor ones by a higher star
formation efficiency and starburst frequency. Low-mass galaxies experienced a
few bursts of star formation whereas massive spiral galaxies experienced
numerous and extended powerful starbursts (abridged version).
