Quantitative constraints on starburst cycles in galaxies with stellar masses in the range 10**8-10**10 Msol

We have used 4000 \AA\ break and H$\delta_A$ indices in combination with SFR/M* derived from emission line flux measurements, to constrain the recent star formation histories of galaxies with stellar masses in the range 10**8-10**10 Msol. The fraction of the total SFR density in galaxies with ongoing bursts is a strong function of stellar mass, declining from 0.85 at a stellar mass of 10**8 Msol to 0.25 for galaxies with M* = 10**10 Msol. Low mass galaxies are not all young. The distribution of half mass formation times for galaxies with stellar masses less than 10**9 Msol is broad, spanning the range 1-10 Gyr. The peak-to-trough variation in star formation rate among the bursting population ranges lies in the range 10-25. In low mass galaxies, the average duration of the burst is comparable to the dynamical time of the galaxy. Galaxy structure is correlated with estimated burst mass fraction, but in different ways in low and in high mass galaxies. High mass galaxies with large burst mass fractions are more centrally concentrated, indicating that bulge formation is at work. In low mass galaxies, stellar surface mass densities decrease as a function of F_{burst}. These results are in good agreement with the observational predictions of Teyssier et al (2013) and lend further credence to the idea that the cuspy halo problem can be solved by energy input from multiple starbursts over the lifetime of the galaxy. We note that there is no compelling evidence for IMF variations in the population of star-forming galaxies in the local Universe.