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Abstract:
We present numerical studies on pattern formation in the excitable region of an electrochemical model that was originally proposed to reproduce nonlinear phenomena observed during the dissolution of metals that exhibit an active–passive transition. The simulations are done employing a realistic three-dimensional geometry of the electrochemical cell. To shed light on the role of the boundary condition at the working electrode (WE), two different arrangements of a disk-shaped WE are considered. In the first case, the WE is surrounded by the cell walls, i.e., it occupies the entire bottom of the cell; in the second case it is embedded in an insulator. For these two arrangements, the typical excitable situation in which the steady state is globally attracting is compared with a situation in which the stable stationary state is close to a subcritical Hopf bifurcation and coexists with a stable limit cycle. For both parameter regions, the response of the system is fundamentally different for the two geometries and differs also from the one typically encountered in a classical reaction–diffusion system with excitable dynamics.
