On the application of the logistic differential equation in electrochemical dynamics

The relevance of the logistic differential equation to the dynamics of the electrochemical intercalation and adsorption/desorption processes postulated recently in this Journal by Gonzales et al. (461 (1999) 161) and confirmed and elaborated soon after by Montella et al. (475 (1999) 190), is challenged. The equations postulated there are not evolution equations in terms of system dynamics but rather limiting forms valid in the special case of linear potential scan and a fully reversible or irreversible process conforming to the Langmuir isotherm. No reaction mechanism requiring replacement of the conventional kinetic equations by the logistic equation was reported. It is recalled here that peculiarities of the logistic equation such as bifurcation, period doubling and chaos are manifested only by its numerical approximation i.e. by the corresponding difference equation used as the real transformation (map) of the interval (0, 1) in the dynamics of discrete systems. These peculiarities do not appear for the continuous form of the logistic differential equation having closed form solution and describing continuous evolution towards the single stable equilibrium point at 1.0.