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Locating unstable periodic orbits in recurrence plots

, 2003
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The Visual Boundary Recurrence Plot: A Closer Look into the Dynamics of Recurrence Plots

International Journal of Bifurcation and Chaos, 2022
In this paper, we introduce a new graphical tool, the visual boundary recurrence plot, in order to provide a more detailed visualization of the well-established method of recurrence plots. In this approach, we are coloring each point of the recurrence plot depending on whether the neighboring points in the vertical and horizontal directions are ...
Athanasios D. Fragkou, Ioannis Andreadis, Theodoros E. Karakasidis   +2 more
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Spatial recurrence plots

Physical Review E, 2006
We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot.
Vasconcelos, D. B., Lopes, S. R., Viana, R. L., Kurths, Jürgen (Prof. Dr.)   +3 more
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Multivariate recurrence plots

Physics Letters A, 2004
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Romano, M., Thiel, M., Kurths, J., von Bloh, W.   +3 more
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RECURRENCE QUANTIFICATIONS: FEATURE EXTRACTIONS FROM RECURRENCE PLOTS

International Journal of Bifurcation and Chaos, 2007
Recurrence plots are two-dimensional representations of multidimensional dynamics captured by applying time delays to a single series (vector) of ordinal data in time or space. Recurrence plots may be presented with beautiful lace-like structures, but most important is the inference these patterns make about the underlying dynamics.
Webber, Charles L. jun., Zbilut, Joseph P.   +1 more
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Entropy of weighted recurrence plots

Physical Review E, 2014
The Shannon entropy of a time series is a standard measure to assess the complexity of a dynamical process and can be used to quantify transitions between different dynamical regimes. An alternative way of quantifying complexity is based on state recurrences, such as those available in recurrence quantification analysis.
Eroglu, D., Peron, T., Marwan, N., Rodrigues, F., Costa, L., Sebek, M., Kiss, I., Kurths, J.   +7 more
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Devaney’s chaos on recurrence plots

Physical Review E, 2010
Although the definition of deterministic chaos in the sense of Devaney is often employed for investigating dynamical systems, it has been rarely used for identifying deterministic chaos from time series. In this paper, we develop a set of methods that infers whether a given time series is consistent with deterministic chaos in the sense of Devaney or ...
Yoshito, Hirata, Kazuyuki, Aihara
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Recurrence plots and unstable periodic orbits

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2002
A recurrence plot is a two-dimensional visualization technique for sequential data. These plots are useful in that they bring out correlations at all scales in a manner that is obvious to the human eye, but their rich geometric structure can make them hard to interpret.
Elizabeth, Bradley, Ricardo, Mantilla
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Recurrence plots of neuronal spike trains

Biological Cybernetics, 1993
The recently developed qualitative method of diagnosis of dynamical systems-recurrence plots-has been applied to the analysis of dynamics of neuronal spike trains recorded from cerebellum and red nucleus of anesthetized cats. Recurrence plots revealed robust and common changes in the similarity structure of interspike interval sequences as well as ...
P, Kałuzny, R, Tarnecki
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Coarse-graining time series data: Recurrence plot of recurrence plots and its application for music

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2016
We propose a nonlinear time series method for characterizing two layers of regularity simultaneously. The key of the method is using the recurrence plots hierarchically, which allows us to preserve the underlying regularities behind the original time series. We demonstrate the proposed method with musical data.
Fukino, Miwa, Hirata, Yoshito, Aihara, Kazuyuki   +2 more
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