Multivariate recurrence plots
@article{Romano2004MultivariateRP,
title={Multivariate recurrence plots},
author={M. C. Romano and Marco Thiel and J{\"u}rgen Kurths and Werner von Bloh},
journal={Physics Letters A},
year={2004},
volume={330},
pages={214-223},
url={https://api.semanticscholar.org/CorpusID:5746162}
}147 Citations
Analytical Description of Recurrence Plots of Dynamical Systems with Nontrivial Recurrences
- 2007
Physics
Recurrence plots are studied for the simplest example of nontrivial recurrences, namely in the case of a quasiperiodic motion, and the understanding of such microscopic structures is important for choosing an appropriate threshold ∊ to analyze experimental data by means of RPs.
Complex Network Analysis of Recurrences
- 2015
Physics
A complex network-based approach to characterizing the geometric properties of chaos by exploiting the pattern of recurrences in phase space and re-interpret the recurrence plot as a graphical representation of the adjacency matrix of a random geometric graph governed by the system’s invariant density.
Geometric detection of coupling directions by means of inter-system recurrence networks
- 2012
Environmental Science, Physics
Local Minima-Based Recurrence Plots for Continuous Dynamical Systems
- 2011
Physics
An alternative procedure for creating RPs using the local minima provided by the distance profile, which approximately corresponds to the recurrence information in the orthogonal direction, is suggested, which yields a clean RP of minimized line thickness.
Trends in recurrence analysis of dynamical systems
- 2023
Computer Science, Physics
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot-based data analysis and to widen its application potential, and open questions and perspectives for futures directions of methodical research are shown.
Recurrence-based time series analysis by means of complex network methods
- 2011
Computer Science, Physics
Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and substantially enrich the knowledge gathered from other existing approaches.
Recurrence Plots and the Analysis of Multiple Spike Trains
- 2014
Computer Science
Some definitions of distances between windows of spike trains are reviewed, methods developed on recurrence plots are explained, and how these plots reveal spike train properties by analysis of simulated and experimental data are illustrated.
Heterogeneous recurrence monitoring and control of nonlinear stochastic processes.
- 2014
Engineering, Mathematics
Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.
Recurrence Plots
- 2020
Physics
Results show that RP method could discriminate: a) attractor-driven oscillation patterns of the transient EEG phenomena during transitions towards deep sleep, visually represented by slow wave sleep (SWS) and expression of EEG synchronization; b) the loss of this attractor -driven oscillations several seconds before the occurrence of REM phases.
42 References
Estimation of dynamical invariants without embedding by recurrence plots.
- 2004
Physics
Two dynamical invariants, the second order Renyi entropy and the correlation dimension, can be estimated from recurrence plots (RPs) with arbitrary embedding dimension and delay with robust results.
Phase synchronization of chaotic oscillators.
- 1996
Physics
The new effect of phase synchronization of weakly coupled self-sustained chaotic oscillators is presented, and a relation between the phase synchronization and the properties of the Lyapunov spectrum is studied.
Cross recurrence plot based synchronization of time series
- 2002
Geology
The method of recurrence plots is extended to the cross recurrence plots (CRP) which, among others, enables the study of synchronization or time differences in two time series. This is emphasized in…
Loss of lag synchronization in coupled chaotic systems.
- 1999
Physics
This work studies transitions to and between different forms of synchronization for the attractors defined as "in-phase" and "out-of- phase" and investigates the processes by which lag synchronization is lost in two coupled Rössler systems.
Manuscript Title: Recurrence Plot Based Measures of Complexity and Its Application to Heart Rate Variability Data
Medicine
Applying new measures of complexity based on vertical structures in recurrence plots and to heart rate variability data, they are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event.
From Phase to Lag Synchronization in Coupled Chaotic Oscillators
- 1997
Physics
We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the…
Nonlinear analysis of bivariate data with cross recurrence plots
- 2002
Physics, Environmental Science
Phase Synchronization of Chaotic Oscillators by External Driving
- 1997
Physics
We extend the notion of phase locking to the case of chaotic oscillators. Different definitions of the phase are discussed, and the phase dynamics of a single self-sustained chaotic oscillator…





