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Spurious Structures in Recurrence Plots Induced by Embedding

Abstract

In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rössler system to show the relevance of this effect.

In the second part of the paper we show that the second order Rényi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay.

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Correspondence to Marco Thiel.

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Thiel, M., Romano, M.C. & Kurths, J. Spurious Structures in Recurrence Plots Induced by Embedding. Nonlinear Dyn 44, 299–305 (2006). https://doi.org/10.1007/s11071-006-2010-9

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Key Words

  • data analysis
  • recurrence plots