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Numerical and analytical study of bifurcations in a model of electrochemical reactions in fuel cells. (English) Zbl 1319.34064

Summary: The bifurcations in a three-variable ODE model describing the oxygen reduction reaction on a platinum surface is studied. The investigation is motivated by the fact that this reaction plays an important role in fuel cells. The goal of this paper is to determine the dynamical behaviour of the ODE system, with emphasis on the number and type of the stationary points, and to find the possible bifurcations. It is shown that a non-trivial steady state can appear through a transcritical bifurcation, or a stable and an unstable steady state can arise as a result of saddle-node bifurcation. The saddle-node bifurcation curve is determined by using the parametric representation method, and this enables us to determine numerically the parameter domain where bistability occurs, which is important from the chemical point of view.

MSC:

34C23 Bifurcation theory for ordinary differential equations
92-08 Computational methods for problems pertaining to biology
92E99 Chemistry
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
78A57 Electrochemistry
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