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Extensive areas in arid and semi-arid regions of the world are covered by sand dunes. Sand dunes can be active, semi-active, or stable, depending on, among other factors, their vegetation and biogenic crust covers. Vegetation growth on barchan dunes can induce a transformation to parabolic dunes with long trailing arms pointed upwind. Here we propose a vegetation dynamical model, coupled to a previously suggested 3D continuous dune morphology model (Duran and Herrmann, 2006). The modeled vegetation reduces sand flux, but it is also suppressed by erosion and by sand deposition. The coupling between the model for bare dunes and the model for vegetation growth is performed by reducing the shear stress due to the presence of vegetation. We use the suggested model to study the effect of vegetation on dune formation, concentrating on the previously simulated barchan-parabolic dune transition. Under the action of sufficiently strong unidirectional winds and a low vegetation growth rate, the model results in a barchan dune. When the vegetation growth rate is increased, the barchan dune turns into a stable parabolic dune. When, however, the growth rate is again decreased, the dune becomes an active barchan dune, only with a much lower growth rate, indicating the existence of bistability and hysteresis behavior of barchan and parabolic dunes under similar climatic (vegetation growth rate or precipitation) conditions.