Desertification is becoming an increasingly serious issue due to both global climate change and the direct anthropogenic destructions on vegetation cover. One type of desertification that caused by vegetation-trapping sand in shrubby areas has been underestimated. In order to explain this situation, we present a dynamic vegetation and aeolian sand model. Through stability analysis of the model, we prove that vegetation can coexist stably with sand deposition, but there is still potential risk of desertification. And for light desertification caused by sand deposition, increasing vegetation cover can help the restoration. Through the model, we assess the potential desertification risk and the difficulty of restoration. Then we couple three typical states of the model to potential desertification, light desertification and severe desertification respectively in desertification process, and to restored, easy reversible, irreversible respectively in vegetation restoration. This coupling helps to understand the interactions between vegetation and sand, and also gives an important holistic picture of model, desertification, and restoration.
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