scholarly journals Application of Recurrence Quantification Analysis for Non-Linear Dynamical Systems

2019 ◽  
Vol 9 (1S5) ◽  
pp. 92-94
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Dynamical Systems ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Recurrence Plots ◽  
Space Trajectories ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Phase Space Trajectories

The Recurrence plots (RPs) have been introduced in several different scientific and medical disciplines. The main purpose of recurrence plot is used to of identify the higher dimensional phase space trajectories. RPs are purely graphically representation which have been designed for the detection of hidden dynamical patterns and non-linearity present in the data, the evaluation of error which is caused by observational noise can be done by Recurrence Quantification Analysis (RQA). RQA method is initially used to minimize the error present in the given signals. RQA method is a basically a technique for the analysis of nonlinear data to quantify the number and duration of a dynamical systems. The recurrence plot is used for time series domain for multidimensional signal also. Recurrence is the property of non-stationary and dynamical system to characteristics the time series analysis in phase space trajectories. Recurrence Quantification Analysis is used to derive from recurrence plots, which are based upon distances matrices of time series.

scholarly journals Nonlinear analysis of gravitational wave signals based on recurrence quantification analysis

2018 ◽  
Vol 210 ◽  
pp. 05011
Author(s):  
Zhenyan Fan ◽  
Qianqian Chen ◽  
Guiqi Sun ◽  
Nikos Mastorakis ◽  
Xiaodong Zhuang
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Gravitational Wave ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Recurrence Plots ◽  
Characteristic Parameters ◽  
Recurrence Quantification ◽  
Movement Characteristic ◽  
Quantification Analysis

Recurrence plot and recurrence quantification analysis are used to analyze different features of gravitational wave signals. Firstly, the appropriate delay time and embedding dimension are respectively estimated by methods of the C_C method. One dimension time series of gravitational wave is extended to high dimension phase space by employing phase space reconstruction for studying the movement characteristic of neighboring points in time series. Then the recurrence plots of different gravitational wave signals are implemented intuitively and qualitatively analyzing different features of gravitational wave signals. Different nonlinear characteristic parameters are calculated by recurrence quantification analysis (RQA) methods, such as recurrence rate, recurrence entropy, determinism rate and stratification, based on which the features of different gravitational wave signals can be well analyzed quantitatively.

Recurrence Plot and Recurrence Quantification of the Dynamic Properties of Cross-Shaped Laminated Energy Harvester

2016 ◽  
Vol 849 ◽  
pp. 95-105 ◽  
Author(s):  
Peter Harris ◽  
Grzegorz Litak ◽  
Joanna Iwaniec ◽  
Chris R. Bowen
Keyword(s):  
Power Output ◽  
Dynamic Properties ◽  
Electrical Power ◽  
Mechanical Vibration ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Recurrence Plots ◽  
Recurrence Quantification ◽  
Time Histories ◽  
Quantification Analysis

The paper examines the dynamic properties of bistable cross-shaped laminate plates for broadband energy harvesting applications by converting mechanical vibration energy into the electrical power output. Bistable laminates plates coupled to piezoelectric transducers were excited by application of harmonic excitations and exhibited a range of vibration patterns. The vibration patterns included single-well oscillations and snap-through vibrations of both periodic and chaotic character; such vibration patterns led to a different power output. Classical spectral analysis of measured voltage, displacement and velocity time histories indicated the presence of a variety of nonlinear and chaotic phenomena. As a result, an analysis of the measured displacement and voltage time histories was carried out with the use of the Recurrence Plots and the Recurrence Quantification Analysis methods. The Recurrence Plots method was used for detection of qualitative changes in the dynamic behaviour of the non-linear harvesting system. In order to facilitate interpretation of piezoelectric voltage and laminate displacement, a detailed analysis using Recurrence Plots, Recurrence Quantification Analysis was employed.

Multiscale Cross-Recurrence Plot and Recurrence Quantification Analysis Based on Coarse-Grained

2021 ◽  
pp. 2150037
Author(s):  
A. Jingjing Huang ◽  
B. Danlei Gu ◽  
C. Qian He
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Real World ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Coarse Grained ◽  
Internal Dynamic ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Different Time Scales

In this paper, we proposed multiscale cross-recurrence quantification analysis (MSCRQA) method to analyze the dynamic states of two time series at different time scales. We apply this method to model system (two coupled van der Pol oscillators) and real-world system (SSEC and SZSE). It demonstrates that the MSCRQA can show richer and more recognizable information compared with single time scale. The state of dynamics is different under different time scales. MSCRQA method shows another multiscale perspective to fully mine more hidden internal dynamic information of a time series. This method may provide another method reference for practical application to better explore the laws of the real world.

scholarly journals HOW TO AVOID POTENTIAL PITFALLS IN RECURRENCE PLOT BASED DATA ANALYSIS

2011 ◽  
Vol 21 (04) ◽  
pp. 1003-1017 ◽  
Author(s):  
NORBERT MARWAN
Keyword(s):  
Data Analysis ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
The Other ◽  
Recurrence Plots ◽  
Deep Foundation ◽  
Recurrence Quantification ◽  
Potential Problems ◽  
Quantification Analysis ◽  
The One

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 for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis.

Recurrence quantification analysis for detecting dynamical changes in earthquake magnitude time series

2015 ◽  
Vol 26 (07) ◽  
pp. 1550077 ◽  
Author(s):  
Min Lin ◽  
Gang Zhao ◽  
Gang Wang
Keyword(s):  
Time Series ◽  
Main Shock ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Confidence Levels ◽  
Aftershock Sequences ◽  
Recurrence Quantification ◽  
Before And After ◽  
Quantification Analysis ◽  
Simultaneous Change

In this study, recurrence plot (RP) and recurrence quantification analysis (RQA) techniques are applied to a magnitude time series composed of seismic events occurred in California region. Using bootstrapping techniques, we give the statistical test of the RQA for detecting dynamical transitions. From our results, we find the different patterns of RPs for magnitude time series before and after the M6.1 Joshua Tree Earthquake. RQA measurements of determinism (DET) and laminarity (LAM) quantifying the order with confidence levels also show peculiar behaviors. It is found that DET and LAM values of the recurrence-based complexity measure significantly increase to a large value at the main shock, and then gradually recovers to a small values after it. The main shock and its aftershock sequences trigger a temporary growth in order and complexity of the deterministic structure in the RP of seismic activity. It implies that the onset of the strong earthquake event is reflected in a sharp and great simultaneous change in RQA measures.

scholarly journals Recurrence quantification analysis of São Francisco River flow: hydrological alterations caused by the construction of Sobradinho dam

2020 ◽  
Vol 9 (11) ◽  
pp. e87491110467
Author(s):  
Leika Irabele Tenório de Santana ◽  
Ikaro Daniel de Carvalho Barreto ◽  
Lidiane da Silva Araújo ◽  
Tatijana Stosic
Keyword(s):  
River Flow ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Dam Construction ◽  
Sao Francisco River ◽  
Daily Streamflow ◽  
São Francisco River ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Daily Streamflow Time Series

We investigated how the construction of the Sobradinho dam and reservoir affected the daily streamflow of the São Francisco River, using the method of Recurrence plot (RP) and Recurrence quantification analysis (RQA) which serves to visualize and quantify the recurrences of the states in the phase space of the dynamic system. We analyzed daily streamflow time series recorded in the fluviometric station Juazeiro that is located downstream of the Sobradinho dam, for the periods before (1943-1972) and after (1980-2009) the dam construction. We observed that in the natural regime, before the dam construction, the streamflow dynamics shows characteristics of periodic and quasi-periodic process, indicated by the checkerboard patterns in RP. After the dam construction, streamflow dynamics exhibit sudden changes indicated by white bands in RP, and become less predictable, less complex, and remain s in certain laminar states for shorter periods, indicated by the decrease of the values of RQA parameters.

Recurrence Quantification Analysis of Financial Markets

2013 ◽  
pp. 50-62
Author(s):  
João A. Bastos
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Recurrence Quantification Analysis ◽  
Government Bonds ◽  
Financial Time ◽  
Analysis Technique ◽  
Recurrence Quantification ◽  
Us Government ◽  
Minimum Number ◽  
Quantification Analysis

Recurrence quantification analysis is a nonlinear time series analysis technique that detects deterministic dependencies in time series. This technique is particularly appropriate for modeling financial time series since it requires no assumptions on stationarity, statistical distribution, and minimum number of observations. This chapter illustrates two applications of recurrence quantification analysis to financial data: a set of international stock indices, and zero-coupon yields of US government bonds.

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