A hierarchy of transitions to mixed mode oscillations in an electrochemical system

Abstract

The dynamic behavior of the electrocatalytic oxidation of hydrogen on a platinum anode in the presence of Cu 2+ and Cl − ions under galvanostatic conditions has been studied experimentally in two control parameters: current density and copper ion concentration. This parameter plane can roughly be divided into three broad regions: A steady state is found at low values of the current density, at medium values the system shows small amplitude oscillations, whereas at high current densities typical mixed mode oscillations (MMOs) are found. Depending on the Cu 2+ concentration, the transition from the small amplitude to the mixed mode regime takes place from a simple periodic, period doubled, or chaotic attractor arising from a Feigenbaum route. In this paper we focus on the characteristics of these different transitions to MMOs and try to construct a bifurcation diagram. The bifurcation from the small chaotic attractor to MMOs very likely constitutes an interior crisis (a bifurcation at which the small chaotic attractor is destroyed by colliding with a stable manifold of a saddle type limit set). At lower copper ion concentrations, the transition to MMOs moved through the period-double cascade. We compile different properties of the bifurcation diagram and discuss a scenario which fits the observations in a consistent way.