We study the stability properties of isolated star forming dwarf galaxies which undergo dynamically driven starbursts induced by stellar feedback. Here we focus on the impact of the adopted ISM model, i.e. either a diffuse or a clumpy ISM. We apply a one-zone model extended for active dynamical evolution. We found two major types of repetitive star bursts: one set (type A) of quasi-periodic starbursts is related to the dynamical timescale of the galaxy. In that case, the star formation follows the variations of the gas density induced by decaying virial oscillations. The second set (type B) of starbursts is characterized by long quiescence periods given by the sum of the dynamical and the dissipative timescale: after a first burst, the inserted energy leads to a substantial expansion of the system, by this stopping any significant star formation activity. A next burst might occur, when the gas reaches high densities again, i.e. after the gas recollapsed and the energy injected by stellar feedback is dissipated. In case of a diffuse ISM model, type A bursts are the most common type due to the high efficiency of radiative cooling (no type B bursts are found). Bursts occur then mainly during an initial transitory phase. In case of a clumpy ISM model (i.e. dissipation by inelastic cloud-cloud collisions), the dissipative timescale is of the order of the dynamical time or longer. This allows for both, type A and type B bursts.