Analytic solution for the electrocatalytic oxidation of formic acid

A model for the electrocatalytic oxidation of formic acid is investigated. Because the reaction rates follow mass action and the Butler-Volmer rate law, the system is highly nonlinear. It is shown that the system can be solved analytically using recent methods from convex and toric geometry, enabling an exact stability analysis without fixing the kinetic parameters. The basic idea is to consider the set of positive stationary reaction rates in convex coordinates and to take into account some further binomial restrictions. This allows us to reduce the dimension of the set of positive stationary solutions and to represent the resulting curve in the concentration space. Many conclusions concerning stability can then be made by geometric considerations. The aim of this paper is to exploit these new methods and to demonstrate their advantage in solving the stability problem for electrochemical systems.