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Critical recurrence scale thresholds
  • Fotios Kasolis ,
  • Markus Clemens
Fotios Kasolis
University of Wuppertal

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Markus Clemens
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Abstract

Recurrence-based studies are employed for determining dynamical properties and for analyzing and processing time-series. Such studies rely on the so-called recurrence matrix, which is an orbit-specific binary representation of a proximity relation on the phase space. Customarily, this state proximity relation is deduced from the underlying metric structure via thresholding, and hence, a single user parameter is required for forming a recurrence matrix, unless embeddings are used. Since most of the prescriptions that can be found in the literature for identifying a suitable recurrence threshold are either heuristic or task-specific, a scaling-analysis framework, which identifies critical scales that emerge during the evolution based on the entropy of maximum sojourn time probability vectors, is introduced and validated here.