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Abstract

We use nonlinear signal processing techniques, based on artificial neural networks, to construct a continuous-time model (set of ordinary differential equations, ODEs) from experimental observations of mixed-mode oscillations during the galvanostatic oxidation of hydrogen on platinum in the presence of bismuth and chloride ions. The data was in the form of time-series of the potential for different values of the applied current and chloride ion concentration. We use the model to reconstruct the experimental dynamics and to explore the associated bifurcation structures in phase-space. Using numerical bifurcation techniques we locate stable and unstable periodic solutions, calculate eigenvalues, and identify bifurcation points. This approach constitutes a promising data post-processing procedure for investigating phase-space and parameter space of real experimental systems; it allows us to infer phase-space structures which the experiments can only probe with limited measurement precision and only at a discrete number of operating parameter settings. For example, the fitted model suggests the existence of a sub-critical Hopf bifurcation near the range of parameters probed in the experiments; this might explain the experimental difficulty in locating small amplitude simple oscillations.