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

TL;DR

This paper extends a phase dispersion method to analyze cyclic behavior in multidimensional time series, demonstrated on test cases and a large-scale solar dynamo simulation, enabling better cycle length estimation in complex systems.

Contribution

It generalizes the D2 phase dispersion statistic for multidimensional data, specifically for analyzing outputs from 3D magnetohydrodynamic simulations.

Findings

Successfully applied to a semi-global solar dynamo simulation with 150 cycles.

Enhanced the ability to estimate cycle lengths in non-linear, multidimensional systems.

Validated the method with simple test cases.

Abstract

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 sys- tems 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.