Recurrence Plots of Dynamical Systems

Eckmann, J. -., Kamphorst, S. O., & Ruelle, D. (1987). Recurrence Plots of Dynamical Systems. Europhysics Letters, 4(9), 973-977.

Type

Journal article

Intellectual base

Primary research

Year

1987

Volume

4

Issue

9

Pages

973-977

ISSN

0295-5075

DOI

10.1209/0295-5075/4/9/004

DOI registrant

IOP Publishing

Link

https://doi.org/10.1209/0295-5075/4/9/004

Cited from

mathematics

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Recurrence
  • A recurrence is distinguished from a mere repetition by the presence of structural echoes—each occurrence shares measurable dependencies or features with prior occurrences—and from periodicity by relaxing the requirement for fixed, regular intervals, an operational distinction Eckmann, Kamphorst, and Ruelle (1987) make precise in their formalization of recurrence plots.

    This sourceFoundational paper introducing recurrence plots: formalizes recurrence as state-space proximity rather than fixed-period repetition, distinguishing it operationally from strict periodicity.

Domain-specific

• Recurrence plot
  • A recurrence plot represents the recurrence matrix R_ij = Θ(ε−||x_i−x_j||), exposing returns, diagonal trajectories, laminar segments, transitions, and nonstationarity in state-space dynamics.

Verification

Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Not recorded. Neither this nor any other of the 2 citations of this work carries a recorded support check.

Was it audited? Yes. A second, independent pass read the citation against the article text and recorded a verdict.

Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.

See how references were verified.

Registry ID ref:1a979c873f53 · see in the full table