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Granger Causality and Cross Recurrence Plots in Rheochaos  [PDF]
Rajesh Ganapathy,Govindan Rangarajan,A. K. Sood
Physics , 2007, DOI: 10.1103/PhysRevE.75.016211
Abstract: Our stress relaxation measurements on wormlike micelles using a Rheo-SALS (rheology + small angle light scattering) apparatus allow simultaneous measurements of the stress and the scattered depolarised intensity. The latter is sensitive to orientational ordering of the micelles. To determine the presence of causal influences between the stress and the depolarised intensity time series, we have used the technique of linear and nonlinear Granger causality. We find there exists a feedback mechanism between the two time series and that the orientational order has a stronger causal effect on the stress than vice versa. We have also studied the phase space dynamics of the stress and the depolarised intensity time series using the recently developed technique of cross recurrence plots (CRPs). The presence of diagonal line structures in the CRPs unambiguously proves that the two time series share similar phase space dynamics.
Recurrence plots of sunspots, solar flux and irradiance  [PDF]
Amelia Sparavigna
Physics , 2008,
Abstract: The paper shows the recurrence and cross recurrence plots of three time series, concerning data of the solar activity. The data are the sunspot number and the values of solar radio flux at 10.7 cm and of solar total irradiance, which are known as highly correlated. To compare the series, the radio flux and irradiance values are monthly averaged. Recurrence plots display the oscillating behaviour with remarkable features. Moreover, cross recurrence plots help in identifying time lags between the sunspot number maximum and the maximum of radio or irradiance signals, in circumstances where the data values are highly dispersed. Image processing is useful too, in enhancing the monitoring. An interesting behaviour is displayed by cross recurrence plots of irradiance, which are not symmetric with respect to the line of identity.
Nonlinear analysis of bivariate data with cross recurrence plots  [PDF]
N. Marwan,J. Kurths
Physics , 2002, DOI: 10.1016/S0375-9601(02)01170-2
Abstract: We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal structures in CRPs. The CRP analysis of prototypical model systems with nonlinear interactions demonstrates that this technique enables to find these nonlinear interrelations from bivariate time series, whereas linear correlation tests do not. Applying the CRP analysis to climatological data, we find a complex relationship between rainfall and El Nino data.
Recurrence plots of exchange rates of currencies  [PDF]
Amelia Carolina Sparavigna
Quantitative Finance , 2014, DOI: 10.18483/ijSci.545
Abstract: Used to investigate the presence of distinctive recurrent behaviours in natural processes, the recurrence plots can be applied to the analysis of economic data, and, in particular, to the characterization of exchange rates of currencies too. In this paper, we will show that these plots are able to characterize the periods of oscillation and random walk of currencies and enhance their reply to news and events, by means of texture transitions. The examples of recurrence plots given here are obtained from time series of exchange rates of Euro.
Recurrence plots from altimetry data of some lakes in Africa  [PDF]
Amelia Carolina Sparavigna
Physics , 2014, DOI: 10.18483/ijSci.534
Abstract: The paper shows recurrence plots obtained from time series of the level variations of four lakes in Africa (Nasser, Tana, Chad and Kainji). The data, coming from remote sensing, are provided by the United States Department of Agriculture. The recurrence plots allow a good visual comparison of the behaviours of local drainage basins.
The Role of Recurrence Plots in Characterizing the Output-Unemployment Relationship: An Analysis  [PDF]
Petre Caraiani, Emmanuel Haven
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0056767
Abstract: We analyse the output-unemployment relationship using an approach based on cross-recurrence plots and quantitative recurrence analysis. We use post-war period quarterly U.S. data. The results obtained show the emergence of a complex and interesting relationship.
Recurrence Plots of Heart Rate Signals during Meditation
Ateke Goshvarpour,Atefeh Goshvarpour
International Journal of Image, Graphics and Signal Processing , 2012,
Abstract: The current study analyses the dynamics of the heart rate signals during specific psychological states in order to obtain a detailed understanding of the heart rate patterns during meditation. In the proposed approach, heart rate time series available in Physionet database are used. The dynamics of the signals are then analyzed before and during meditation by examining the attractors in the phase space and recurrence quantification analysis. In general, the results reveal that the heart rate signals transit from a chaotic, highly-complex behavior before meditation to a low dimensional chaotic (and quasi-periodic) motion during meditation. This can be due to decreased nonlinear interaction of variables in meditation states and may be related to increased parasympathetic activity and increase of relaxation state. The results suggest that nonlinear chaotic indices may serve as a quantitative measure for psychophysiological states.
Recurrence Plots 25 years later -- gaining confidence in dynamical transitions  [PDF]
Norbert Marwan,Stefan Schinkel,Jürgen Kurths
Physics , 2013, DOI: 10.1209/0295-5075/101/20007
Abstract: Recurrence plot based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots.
Analytical description of Recurrence Plots of white noise and chaotic processes  [PDF]
M. Thiel,M. C. Romano,J. Kurths
Physics , 2003,
Abstract: We present an analytical description of the distribution of diagonal lines in Recurrence Plots (RPs) for white noise and chaotic systems, and find that the latter one is linked to the correlation entropy. Further we identify two scaling regions in the distribution of diagonals for oscillatory chaotic systems that are hinged to two prediction horizons and to the geometry of the attractor. These scaling regions cannot be observed with the Grassberger-Procaccia algorithm. Finally, we propose methods to estimate dynamical invariants from RPs.
Recurrence plots and chaotic motion around Kerr black hole  [PDF]
Ond?ej Kopá?ek,Ji?í Ková?,Vladimír Karas,Zdeněk Stuchlík
Physics , 2010, DOI: 10.1063/1.3506071
Abstract: We study the motion of charged test particles around a Kerr black hole immersed in the asymptotically uniform magnetic field, concluding that off-equatorial stable orbits are allowed in this system. Being interested in dynamical properties of these astrophysically relevant orbits we employ rather novel approach based on the analysis of recurrences of the system to the vicinity of its previous states. We use recurrence plots (RPs) as a tool to visualize recurrences of the trajectory in the phase space. Construction of RPs is simple and straightforward regardless of the dimension of the phase space, which is a major advantage of this approach when compared to the "traditional" methods of the numerical analysis of dynamical systems (for instance the visual survey of Poincar\'{e} surfaces of section, evaluation of the Lyapunov spectra etc.). We show that RPs and their quantitative measures (obtained from recurrence quantification analysis -- RQA) are powerful tools to detect dynamical regime of motion (regular vs. chaotic) and precisely locate the transitions between these regimes.
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