Based on impedance spectroscopy method the influence of bulk concentration c(0) on the appearance of dynamic instabilities giving rise to periodic current oscillations (Hopf instability) and bistability (saddle-node instability) in a model electrocatalytic process on a spherical electrode surface with a preceding homogeneous chemical reaction in the Nernst diffusion layer under potentiostatic conditions was determined. It was shown that the critical values of the parameter c(0) confined the ranges of the Hopf and saddle-node instabilities are dependent on the effective rate of a preceding chemical reaction k, electrode radius r(0), the Nernst diffusion layer thickness d and the ohmic resistance R-s. Parameters k, d, r(0) and R-s, regulate the ranges of the instabilities in question in an opposite way. There are the parameters values at which a Hopf and a saddle-node instabilities coalesce. The results obtained were compared with that for a planar electrode. (C) 2013 Elsevier Ltd. All rights reserved.