In our earlier report on the experimental studies of convection coupled with electrochemical processes of Hg ions at the mercury electrode we showed that the potential-dependent onset and decay of this convection can give rise to the N-shaped negative differential resistance (NNDR) in the current-potential characteristics. As it consequence, the presence of appropriate serial ohmic resistance ill the electric circuit caused bistability. Since the rather poorly reproducible nature of this convection makes the precise experimental studies difficult, we elaborated the simple model which extracts the basic dynamical properties of the system under study. The model involves the electrode potential and the Nernst layer thickness for the convective diffusion its the dynamical variables. Using linear stability analysis we derived the stability criteria and constructed the bifurcation diagram, showing bistability, in accordance with the experimental data, but not predicting the oscillatory behavior. (c) 2008 Elsevier B.V. All rights reserved.