Spurious structures in recurrence plots induced by embedding. (English) Zbl 1101.82320
Summary: 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 RP with arbitrary embedding dimension and delay.
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 RP with arbitrary embedding dimension and delay.
MSC:
| 82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
| 37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62-07 | Data analysis (statistics) (MSC2010) |
Software:
K2References:
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