In the presence of vegetation, dunes take on specific shapes that can be observed not only on the edges of sandy deserts, but also in coastal areas and arid plains. These vegetated bedforms play a crucial role in preventing desertification and coastal erosion, and are therefore an important social issue in the context of climate change. As for barchans in the absence of vegetation, parabolic dunes can be observed in isolation or in clusters, mainly under unimodal wind regimes in zones of low sediment availability. They are both crescent-shaped, their horns extending in opposite directions on either side of the migrating central body. As both dune types are likely to emerge from each other, the barchan-parabolic transition has been extensively studied, both in the field and using different types of models. By injecting a feedback mechanism between vegetation and sediment transport into ReSCAL (Narteau et al., 2009; Rozier & Narteau, 2014), we propose here a new model for vegetated dunes. From our simulations, we show that parabolic dunes are unstable, systematically increasing or decreasing in size according to the volumes of sediment they deposit upstream in their horns and cannibalise downstream on the vegetated bed they remobilise. Using the same specific boundary conditions over the parameter space of the model, we present the complete diagrams of steady-state dune shape through the barchan-parabolic transition. Between the typical barchan and parabolic shapes, we find that all the diversity of isolated dune forms observed in the field can occur in a steady-state as vegetation stabilises increasingly thick layers of sand. To compensate for an increasing impact of vegetation, the migrating dune body becomes steeper and reverses its curvature so that the lateral sediment fluxes can now provide a positive contribution to aeolian transport in the central layers. Finally, we show that vegetated dunes can undergo smooth hysteretic transitions between steady states, explaining the resilience of parabolic dunes in the field under a wide range of climatic conditions.