  This paper is devoted to the analysis of the uniform null controllability for
a family of nonlinear reaction-diffusion systems approximating a
parabolic-elliptic system which models the electrical activity of the heart.
The uniform, with respect to the degenerating parameter, null controllability
of the approximating system by means of a single control is shown. The proof is
based on the combination of Carleman estimates and weighted energy
inequalities.
