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Recurrence quantification analysis is a widely used method for characterizing patterns in time series. This article presents a comprehensive survey for conducting a wide range of recurrence-based analyses to quantify the dynamical structure…

Data Analysis, Statistics and Probability · Physics 2023-03-30 Moreno I. Coco , Dan Mønster , Giuseppe Leonardi , Rick Dale , Sebastian Wallot

Recurrence Quantification Analysis (RQA) can help to detect significant events and phase transitions of a dynamical system, but choosing a suitable set of parameters is crucial for the success. From recurrence plots different RQA variables…

Signal Processing · Electrical Eng. & Systems 2019-02-08 Georgios Giasemidis , Danica Vukadinovic Greetham

Recurrence plot is a quite easy tool to be used in time series analysis,in particular for measuring unstable periodic orbits embedded in a chaotic dynamical system. Recurrence quantified analysis (RQA) is an advance tool that allows the…

Chaotic Dynamics · Physics 2007-05-23 H. Castellini , L. Romanelli

PyRQA is a software package that efficiently conducts recurrence quantification analysis (RQA) on time series consisting of more than one million data points. RQA is a method from non-linear time series analysis that quantifies the…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-03-03 Tobias Rawald , Mike Sips , Norbert Marwan

Recurrence quantification analysis (RQA) is a well established method of nonlinear data analysis. In this work we present a new strategy for an almost parameter-free RQA. The approach finally omits the choice of the threshold parameter by…

Data Analysis, Statistics and Probability · Physics 2022-11-02 Radim Pánis , Karel Adámek , Norbert Marwan

Test-time compute is central to large reasoning models, yet analysing their reasoning behaviour through generated text is increasingly impractical and unreliable. Response length is often used as a brute proxy for reasoning effort, but this…

Computation and Language · Computer Science 2026-02-09 Quoc Tuan Pham , Mehdi Jafari , Flora Salim

Recurrence plots (RPs) are powerful tools for visualizing time series dynamics; however, traditional Recurrence Quantification Analysis (RQA) often relies on global metrics, such as line counting, that can overlook system-specific,…

Trajectories of units moving on networks are relevant for nonlinear dynamical systems as diverse as polymers, ocean drifters, and human mobility. Although RQA is a well-researched tool with applications in many areas, it has rarely been…

Physics and Society · Physics 2026-04-22 A. Schmaus , N. Marwan , N. Molkenthin

In this paper, we elaborate over the well-known interpretability issue in echo state networks. The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques taken from research on complex systems.…

Data Analysis, Statistics and Probability · Physics 2016-11-21 Filippo Maria Bianchi , Lorenzo Livi , Cesare Alippi

Nowadays, when crashes and crises are rather frequent events, an effective monitoring system for the international financial market is needed. Modern nonlinear methods, such as Recurrence Quantification Analysis (RQA), demonstrate the…

Statistical Finance · Quantitative Finance 2011-12-02 Sergii Piskun , Oleksandr Piskun , Dmitry Chabanenko

Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late…

Chaotic Dynamics · Physics 2025-01-27 Norbert Marwan , Maria Carmen Romano , Marco Thiel , Jürgen Kurths

Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools…

Chaotic Dynamics · Physics 2013-06-05 Norbert Marwan

Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence…

chao-dyn · Physics 2012-08-27 J. P. Zbilut , A. Giuliani , C. L. Webber,

Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) are signal numerical analysis methodologies able to work with non linear dynamical systems and non stationarity. Moreover they well evidence changes in the states of a…

Statistical Mechanics · Physics 2012-10-03 A. Fabretti , M. Ausloos

In this work we explore the possibility of using Recurrence Quantification Analysis (RQA) in astronomical high-contrast imaging to statistically discriminate the signal of faint objects from speckle noise. To this end, we tested RQA on a…

Instrumentation and Methods for Astrophysics · Physics 2018-11-28 M. Stangalini , G. Li Causi , F. Pedichini , S. Antoniucci , M. Mattioli , J. Christou , G. Consolini , D. Hope , S. M. Jefferies , R. Piazzesi , V. Testa

Recurrence Quantification Analysis (RQA) is a widely used method for capturing the dynamical structure embedded in time series data, relying on the analysis of recurrence patterns in the reconstructed phase space via recurrence plots (RPs).…

Chaotic Dynamics · Physics 2026-01-15 Athul Mohan , G. Ambika , Chandrakala Meena

One challenge with the analysis of complex systems and the interaction between such systems is that they are composed of different numbers of components, or simply the fact that a different number of observables is available for each…

Data Analysis, Statistics and Probability · Physics 2025-12-22 Sebastian Wallot , Dan Mønster

In recent years, recurrent quantification analysis (RQA) and its multi-dimensional version (MdRQA) have emerged as a popular tool for assessing interpersonal behavioral or physiological synchrony in groups of two or more individuals. While…

Neurons and Cognition · Quantitative Biology 2023-08-16 Swarag Thaikkandi , K. M. Sharika

Recursive QAOA (RQAOA) solves combinatorial optimization problems by using shallow quantum circuits to estimate pairwise correlations and recursively eliminate variables until a classical solver can handle the residual instance. Each…

Quantum Physics · Physics 2026-05-27 Euimin Lee , Shiho Kim

The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…

Chaotic Dynamics · Physics 2024-11-05 Shivam Kumar , R. Misra , G. Ambika
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