Pérez García, Victor M.. 

We study the stability and dynamics of vortices in two-species condensates using a two-mode model. The recent experimental results obtained at JILA [M. R. Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)] and recent numerical simulations based on the Gross-Pitaevskii equations are explained using this simple model. We also make an exhaustive analysis of the stability properties of the system when the relative populations of the two species and/or their relative scattering lengths are changed and prove that stabilization of otherwise unstable configurations can be attained by controlling the relative population of both species.