Directional search algorithm for electrochemical oscillating time-series in a multidimensional parameter space

Definitely, modeling complex electrochemical reactions is not a trivial task. The reaction kinetics, usually described by several independent variables, can be represented by an intricate combination of elementary steps through parallel and consecutive mechanisms. Because of this complexity, it is also extremely difficult to measure rate constants of the elementary steps experimentally which results in an incomplete knowledge of the parameters that drive the system. Therefore, a numerical integration of the model cannot be carried out since several unknown parameters values still have to be implemented. ln order to overcome this restriction, we have developed a directional search algorithm for oscillating solutions in a multidimensional parameter space. Overall, the code identifies a set of parameters (rate constants, applied voltage, resistance and etc), where oscillatory behavior (potential or current oscillations) is found , by an adaptive scanning. Firstly, the algorithm integrates the differential equations, built from the kinetic rate laws, with a pre-determined set of parameters, then verifies if the output obeys the stablished criteria for a desired solution such as: characteristics of maximum and minimum points, and the convergence (see the flowchart); if not, the code modifies up to three chosen parameters randomically and iterates until the solution fills the selection criteria. lf the criteria are satisfied, concomitantly, the solution is an oscillating behavior, the set of parameters is recorded. lf not, the loop starts over. The algorithm is summarized in the following figure.