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Spurious Structures in Recurrence Plots Induced by Embedding

Research paper by Marco Thiel, M. Carmen Romano, Jürgen Kurths

Indexed on: 01 Jun '06Published on: 01 Jun '06Published in: Nonlinear Dynamics



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.