Dynamical counterexamples regarding the Extremal Index and the mean of the limiting cluster size distribution

Abadi, Miguel; Freitas, Ana Cristina Moreira; Freitas, Jorge Milhazes

doi:10.48550/arxiv.1808.02970

Cited by 1 publication

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“…meaning that x and y are decoupled when D xy = D x + D y , while they are linked via a deterministic function (i.e., exhibit generalized synchronization) when D xy = min(D x , D y ). As for D, the bivariate persistence θ xy can be defined as a weighted average of θ x and θ y [44,45]. Different from the univariate case, an additional new dynamical system metric can be defined in the bivariate case, i.e., the so-called co-recurrence ratio As noted in Faranda et al [44], α cannot be interpreted in terms of causation but only as mutual relation.…”

Section: Dynamical System Metrics For Bivariate Time Seriesmentioning

confidence: 99%

Concurrent Effects between Geomagnetic Storms and Magnetospheric Substorms

et al. 2022

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An accurate understanding of dissimilarities in geomagnetic variability between quiet and disturbed periods has the potential to vastly improve space weather diagnosis. In this work, we exploit some recently developed methods of dynamical system theory to provide new insights and conceptual ideas in space weather science. In particular, we study the co-variation and recurrence statistics of two geomagnetic indices, SYM-H and AL, that measure the intensity of the globally symmetric component of the equatorial electrojet and that of the westward auroral electrojet, respectively. We find that the number of active degrees of freedom, required to describe the phase space dynamics of both indices, depends on the geomagnetic activity level. When the magnetospheric substorm activity, as monitored by the AL index, increases, the active number of degrees of freedom increases at high latitudes above the dimension obtained through classical time delay embedding methods. Conversely, a reduced number of degrees of freedom is observed during geomagnetic storms at low latitude by analysing the SYM-H index. By investigating time-dependent relations between both indices we find that a significant amount of information is shared between high and low latitude current systems originating from coupling mechanisms within the magnetosphere–ionosphere system as the result of a complex interplay between processes and phenomena of internal origin activated by the triggering of external source processes. Our observations support the idea that the near-Earth electromagnetic environment is a complex system far from an equilibrium.

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Section: Dynamical System Metrics For Bivariate Time Seriesmentioning

confidence: 99%