Correlation Dimension Analysis Applied to a Magnetotail Coupled-Map Lattice Model Academic Article uri icon


  • It has been suggested that slowly driven dynamical systems, with many degrees of freedom, self-organise into a critical state, with avalanches of all sizes obeying power law characteristics. Various recent observations and numerical simulations suggest that the Earth's magnetotail system, a highly complex system, could exist in a near-critical configuration. Although no experiment exists to prove entirely that a system is self-organised critical (SOC), several pieces of evidence can be collected to support the idea, e.g. exhibition of power-law scaling in distribution functions. An additional tool that can be used to reveal information from an observed time-series is correlation dimension analysis. The goal of a correlation dimension analysis is to extract, from a highly complex system with many degrees of freedom, the dimension of an underlying chaotic attractor. The existence of such a dimension may be used as evidence to argue whether a system is in a SOC state or otherwise. The numerical simulation used in this work, a magnetic field model of the magnetotail current sheet, has been developed by, amongst others, {Takalo, Timonen et al., (1999)}. It is in the form of a Coupled-Map Lattice (CML) and is based on the MHD diffusion equation and is continuously driven by solar wind vBs data. It has been shown by {Takalo, Timonen et al., (1999)} that the model exhibits perturbations (avalanches) with power-law scalings in their distributions of duration and size. Such distributions may indicate SOC behaviour. This paper presents the results of a correlation dimension analysis of the numerical outputs of the CML model and discusses the implications.

publication date

  • December 1, 2004