  We consider the effects of non-constant star formation histories (SFHs) on
Halpha and GALEX far ultra-violet (FUV) star formation rate (SFR) indicators.
Under the assumption of a fully populated Chabrier IMF, we compare the
distribution of Halpha-to-FUV flux ratios from ~ 1500 simple, periodic model
SFHs with observations of 185 galaxies from the Spitzer Local Volume Legacy
survey. We find a set of SFH models that are well matched to the data, such
that more massive galaxies are best characterized by nearly constant SFHs,
while low mass systems experience bursts amplitudes of ~ 30 (i.e., an increase
in the SFR by a factor of 30 over the SFR during the inter-burst period), burst
durations of tens of Myr, and periods of ~ 250 Myr; these SFHs are broadly
consistent with the increased stochastic star formation expected in systems
with lower SFRs. We analyze the predicted temporal evolution of galaxy stellar
mass, R-band surface brightness, Halpha-derived SFR, and blue luminosity, and
find that they provide a reasonable match to observed flux distributions. We
find that our model SFHs are generally able to reproduce both the observed
systematic decline and increased scatter in Halpha-to-FUV ratios toward low
mass systems, without invoking other physical mechanisms. We also compare our
predictions with those from the Integrated Galactic IMF theory with a constant
SFR. We find that while both predict a systematic decline in the observed
ratios, only the time variable SFH models are capable of producing the observed
population of low mass galaxies ($M_{*}$ < 10$^{7}$ Msun) with normal
Halpha-to-FUV ratios. These results demonstrate that a variable IMF alone has
difficulty explaining the observed scatter in the Halpha-to-FUV ratios. We
conclude by considering the limitations of the model SFHs, and discuss the use
of additional empirical constraints to improve future SFH modeling efforts.
