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It is now a well-established fact that also very low mass stars harbor planetary systems. These stars represent the large majority of our nearby stars but, despite their proximity, their low optical luminosity makes it difficult to apply the usual methods for exoplanet search. An effective probe for the environment of these stars is the auroral radio emission. This kind of emission is well understood for those stars whose magnetic field can be approximated as a dipole. In these cases the radio emission has a peculiar signature in time and in polarization. The presence of a planet nearby the star triggers or perturbs this emission leading to a predictable modulation. We present the case study of the ultra-cool dwarf TVLM 513-46546, for which we take advantage of VLA observations at 4.9 and 8.4 GHz. We reproduce the cyclic circularly-polarized pulses of the star using a 3D model of the auroral radio emission from the stellar magnetosphere. To take into account the possible deviation from the dipolar symmetry, the model simulates a magnetosphere shaped like an offset-dipole. To reproduce the timing and pattern of the observed pulses we explored the space of parameters controlling the auroral beaming pattern and the magnetosphere geometry. Our model explains the observed anomalies of the radio emission at 8.4 GHz as a possible interaction of the star with an external body, like in the case of the interaction between Jupiter and Io.