We study the stability properties of isolated star forming dwarf galaxies which undergo dynamically driven star bursts 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. This allows for a coupling between the dynamical state of the galaxy and its internal properties like star formation activity or the thermal state (or dynamical pressure, respectively) of the interstellar medium (ISM).We found two major types of repetitive star bursts: one set (type A) of quasi-periodic star bursts 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 recurrent star bursts is characterized by a long quiescence period given by the sum of the dynamical and the dissiptional timescale: after a first burst, the inserted energy leads to a substantial expansion of the system, by this stopping any significant SF 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. Whereas initial transitory bursts are quite common, type B bursts are only found in a small mass range for given feedback and dissipation parameters.