The ring system and small satellites of Neptune were discovered during Voyager 2 flyby in 1989 (Smith et al. 1989). In this work we analyse the diffusion maps which can give an overview of the system. As a result we found the width of unstable and stable regions close to each satellite. The innermost Galle ring, which is further from the satellites, is located in a stable region, while Lassel ring (W = 4000 km) has its inner border in a stable region depending on its eccentricity. The same happens to the Le Verrier and Adams rings , they are stable for small values of the eccentricity. They can survive to the close satellites perturbation only for values of e < 0.012. When the solar radiation force is taken into account the rings composed by 1µm sized particles have a lifetime of about 10 4 years while larger particles (10µm in radius) can survive up to 10 5 years. The satellites Naiad, Thalassa and Despina can help replenish the lost particles of the Le Verrier, Arago and Lassel rings, while the ejecta produced by Galatea, Larissa and Proteus do not have enough velocity to escape from the satellite gravity.

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