Method for estimating cycle lengths from multidimensional time series: Test cases and application to a massive “in silico” dataset

Many real world systems exhibit cyclic behavior that is, for example, due to the nearly harmonic oscillations being perturbed by the strong fluctuations present in the regime of significant non-linearities. For the investigation of such systems special techniques relaxing the assumption to periodicity are required. In this paper, we present the generalization of one of such techniques, namely the D² phase dispersion statistic, to multidimensional datasets, especially suited for the analysis of the outputs from three-dimensional numerical simulations of the full magnetohydrodynamic equations. We present the motivation and need for the usage of such a method with simple test cases, and present an application to a solar-like semi-global numerical dynamo simulation covering nearly 150 magnetic cycles.