scholarly journals Chaotic Features of Decomposed Time Series from Tidal River Water Level

2021 ◽  
Vol 12 (1) ◽  
pp. 199
Author(s):  
Myungjin Lee ◽  
Hung Soo Kim ◽  
Jaewon Kwak ◽  
Jongsung Kim ◽  
Soojun Kim
Keyword(s):  
Time Series ◽  
Water Level ◽  
Correlation Dimension ◽  
Chaotic Behavior ◽  
Tidal River ◽  
Stochastic Chaos ◽  
Entropy Information ◽  
Correlation Exponent ◽  
Stochastic Characteristics ◽  
Rainfall Shock

This study assessed the characteristics of water-level time series of a tidal river by decomposing it into tide, wave, rainfall-runoff, and noise components. Especially, the analysis for chaotic behavior of each component was done by estimating the correlation dimension with phase-space reconstruction of time series and by using a close returns plot (CRP). Among the time series, the tide component showed chaotic characteristics to have a correlation dimension of 1.3. It was found out that the water level has stochastic characteristics showing the increasing trend of the correlation exponent in the embedding dimension. Other components also showed the stochastic characteristics. Then, the CRP was used to examine the characteristics of each component. The tide component showed the chaotic characteristics in its CRP. The CRP of water level showed an aperiodic characteristic which slightly strayed away from its periodicity, and this might be related to the tide component. This study showed that a low water level is mainly affected by a chaotic tide component through entropy information. Even though the water level did not show chaotic characteristics in the correlation dimension, it showed stochastic chaos characteristics in the CRP. Other components showed stochastic characteristics in the CRP. It was confirmed that the water level showed chaotic characteristics when it was not affected by rainfall and stochastic characteristics deviating from the bounded trajectory when water level rises due to rainfall. Therefore, we have shown that the water level related to the chaotic tide component can also have chaotic properties because water level is influenced by chaotic tide and rainfall shock, thus it showed stochastic chaos characteristics.

scholarly journals The comparative study of chaoticity and dynamical complexity of the low-latitude ionosphere, over Nigeria, during quiet and disturbed days

2014 ◽  
Vol 21 (1) ◽  
pp. 127-142 ◽  
Author(s):  
B. O. Ogunsua ◽  
J. A. Laoye ◽  
I. A. Fuwape ◽  
A. B. Rabiu
Keyword(s):  
Time Series ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Chaotic Behavior ◽  
Surrogate Data ◽  
Tsallis Entropy ◽  
Electron Content ◽  
Total Electron ◽  
Dynamical Complexity ◽  
Definite Pattern

Abstract. The deterministic chaotic behavior and dynamical complexity of the space plasma dynamical system over Nigeria are analyzed in this study and characterized. The study was carried out using GPS (Global Positioning System) TEC (Total Electron Content) time series, measured in the year 2011 at three GPS receiver stations within Nigeria, which lies within the equatorial ionization anomaly region. The TEC time series for the five quietest and five most disturbed days of each month of the year were selected for the study. The nonlinear aspect of the TEC time series was obtained by detrending the data. The detrended TEC time series were subjected to various analyses for phase space reconstruction and to obtain the values of chaotic quantifiers like Lyapunov exponents, correlation dimension and also Tsallis entropy for the measurement of dynamical complexity. The observations made show positive Lyapunov exponents (LE) for both quiet and disturbed days, which indicates chaoticity, and for different days the chaoticity of the ionosphere exhibits no definite pattern for either quiet or disturbed days. However, values of LE were lower for the storm period compared with its nearest relative quiet periods for all the stations. The monthly averages of LE and entropy also show no definite pattern for the month of the year. The values of the correlation dimension computed range from 2.8 to 3.5, with the lowest values recorded at the storm period of October 2011. The surrogate data test shows a significance of difference greater than 2 for all the quantifiers. The entropy values remain relatively close, with slight changes in these values during storm periods. The values of Tsallis entropy show similar variation patterns to those of Lyapunov exponents, with a lot of agreement in their comparison, with all computed values of Lyapunov exponents correlating with values of Tsallis entropy within the range of 0.79 to 0.81. These results show that both quantifiers can be used together as indices in the study of the variation of the dynamical complexity of the ionosphere. The results also show a strong play between determinism and stochasticity. The behavior of the ionosphere during these storm and quiet periods for the seasons of the year are discussed based on the results obtained from the chaotic quantifiers.

Study on the nonlinear and chaotic behavior of exchange traded funds listed in Hong Kong Stock Exchanges

2020 ◽  
Author(s):  
Patrick Kuok Kun Chu
Keyword(s):  
Time Series ◽  
Hong Kong ◽  
Correlation Dimension ◽  
Model Building ◽  
Chaotic Behavior ◽  
Return Time ◽  
Stock Exchanges ◽  
Garch Models ◽  
Exchange Traded Funds ◽  
Bds Test

This study examines the nonlinearity and chaotic behavior of the time series of returns of two exchange traded funds (ETFs) listed in Hong Kong Stock Exchanges, namely Hong Kong Tracker Fund (HKTF) and iShares FTSE A50 (ISFT), and the adequacy of autoregressive-generalized autoregressive conditional heteroskedasticity (AR-GARCH) models to capture nonlinearity. A set of nonlinearity tests consistently indicates the presence of nonlinearity in both return time series and the Brock–Dechert–Scheinkman (BDS) test of nonlinearity on AR-GARCH residuals, and the inability of AR-GARCH models to capture the nonlinearity in the return series at different stages of the model-building process. Testing for chaos is a rather delicate part in this study and is done by estimating the correlation dimension for both ETFs’ return series. The correlation dimension saturates at a finite value, and the saturation indicates the presence of chaos in two ETFs considered for this study.

scholarly journals Analysis of the Characteristics of Monthly Rainfall Pattern in Katsina

2019 ◽  
pp. 1-13
Author(s):  
Emmanuel Vezua Tikyaa ◽  
Francis Oladele Anjorin ◽  
Emmanuel Joseph
Keyword(s):  
Time Series ◽  
Nonlinear Analysis ◽  
Chaotic Behavior ◽  
Monthly Rainfall ◽  
Skewed Distribution ◽  
Rainfall Pattern ◽  
Largest Lyapunov Exponent ◽  
Rainfall Time Series ◽  
Correlation Exponent ◽  
Increasing Trend

Aims: This paper seeks to analyse the characteristics of monthly rainfall pattern in Katsina City in a view to unveiling the trends and describing its dynamics so that adequate recommendations can be made for its modelling. Study Design: The analysis involves a complete statistical, trend, spectral and nonlinear analysis of the monthly rainfall time series recorded in Katsina. Place and Duration of Study: Location: Katsina City, Katsina State, Nigeria from 1990 to 2015; a period of 26 years. Methodology: Secondary data of daily rainfall recorded in Katsina city from 1990 to 2015 was collected from the Nigerian Meteorological Agency (NiMet), and monthly averages were taken to obtain the monthly rainfall data. The data was then subjected to statistical, trend, spectral and nonlinear analysis techniques to reveal the behavioural patterns in the rainfall and also to reveal its underlying dynamics for its future modelling and prediction. Results: The outcome of this analysis indicates that the monthly rainfall in Katsina exhibits an increasing trend with high variance and right-skewed distribution requiring a maximum of 6 independent variables to model its dynamics. The correlation exponent plot reached a saturation value of 5.892 confirming that the monthly rainfall in Katsina over the last 26 years exhibits low dimensional chaotic behavior while the largest Lyapunov exponent for the monthly rainfall time series in Katsina was also computed and found to be positive, having a value of 0.006055/month confirming the presence of deterministic chaos dynamics and is predictable for the next 165 months. Conclusion: Since from the findings of this work it is confirmed that the rainfall in Katsina exhibits chaotic behavior with an increasing trend, it is recommended that more drainages and dams be built to provide steady supply of water for agricultural and domestic purposes as well as curtail the menace of flooding and drought which may occur as a result of global warming and climate change.

scholarly journals Decomposition of Water Level Time Series of a Tidal River into Tide, Wave and Rainfall-Runoff Components

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1568 ◽  
Author(s):  
Myungjin Lee ◽  
Younghoon You ◽  
Soojun Kim ◽  
Kyung Kim ◽  
Hung Kim
Keyword(s):  
Time Series ◽  
Water Level ◽  
Complex Structure ◽  
Tidal River ◽  
Rainfall Runoff ◽  
Noise Component ◽  
Pass Filter ◽  
Level Data ◽  
Rainfall Runoff Model ◽  
Main Components

The water-level time series of a tidal river is influenced by various factors and has a complex structure, which limits its use as hydrological forecast data. This study proposes a methodology for decomposing the water-level time series of a tidal river into various components that influence the water level. To this end, the tide, wave, rainfall-induced runoff and noise components were selected as the main components that affect the water-level time series. The tide component and the wave component were first separated through wavelet analysis and curve fitting and then they were removed from the water-level data. A high-pass filter was then applied to the resulting time series to separate the rainfall-induced runoff component and the noise component. These methods made it possible to determine the rate of influence that each component has on the water level of a tidal river. The results could be used as a basis for calibrating a rainfall-runoff model and issuing flood forecasts and warnings for a tidal river.

Analysis and Identification of Chaotic Dynamics in a Flying Vibratory System

2004 ◽  
Author(s):  
Jin-Wei Liang ◽  
Shy-Leh Chen ◽  
Ching-Ming Yen
Keyword(s):  
Time Series ◽  
Correlation Dimension ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Random Noise ◽  
Maximum Lyapunov Exponent ◽  
Embedding Dimension ◽  
Vibratory System ◽  
Experimental Time Series ◽  
Acceleration Signals

This paper aims at determining whether chaotic dynamics exist in a flying vibratory system. It is important to identify chaotic behavior in a flying system since it may jeopardize the structure of the flying object and cause instability subsequently. It can also cause uncomfortable experience for passengers in a passenger airplane or inaccurate targeting for a missile. Identification of chaotic dynamics from experimental time series is a nontrivial task, since the data is likely to be contaminated with random noise that possesses similar properties to chaos. In this work, acceleration signals were measured at nine different locations or orientations of the flying object during a test fly. Steady-state acceleration signals were extracted and analyzed. The analysis is based on the pseudo phase-space trajectories reconstructed from the experimental time series using the method of delays. Two indices, the correlation dimension and the maximum Lyapunov exponent, are employed to identify the chaotic behavior and to distinguish it from random noise. In general, the correlation dimension calculated from the pseudo trajectory depends on the embedding dimension. It is found in three of the nine-channel signals that the correlation dimension saturates when the embedding dimension is larger than a critical value. The critical embedding dimension is the minimum dimension required for fully un-stretching the phase-space trajectories. This phenomenon indicates a possible existence of chaotic dynamics. It is also found that the maximum Lyapunov exponents calculated from the same acceleration signals are all positive, which further verifies the possibility of the existence of chaotic motion. In addition, some computational issues regarding the embedding dimension, correlation dimension, and maximum Lyapunov exponent are discussed in this paper.

scholarly journals Chaotic dynamics of cardioventilatory coupling in humans: effects of ventilatory modes

2009 ◽  
Vol 296 (4) ◽  
pp. R1088-R1097 ◽  
Author(s):  
Laurence Mangin ◽  
Christine Clerici ◽  
Thomas Similowski ◽  
Chi-Sang Poon
Keyword(s):  
Time Series ◽  
Correlation Dimension ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Intrathoracic Pressure ◽  
Ventilator Weaning ◽  
Largest Lyapunov Exponent ◽  
Ventilatory Mode ◽  
Limit Value ◽  
Noise Limit

Cardioventilatory coupling (CVC), a transient temporal alignment between the heartbeat and inspiratory activity, has been studied in animals and humans mainly during anesthesia. The origin of the coupling remains uncertain, whether or not ventilation is a main determinant in the CVC process and whether the coupling exhibits chaotic behavior. In this frame, we studied sedative-free, mechanically ventilated patients experiencing rapid sequential changes in breathing control during ventilator weaning during a switch from a machine-controlled assistance mode [assist-controlled ventilation (ACV)] to a patient-driven mode [inspiratory pressure support (IPS) and unsupported spontaneous breathing (USB)]. Time series were computed as R to start inspiration (RI) and R to the start of expiration (RE). Chaos was characterized with the noise titration method (noise limit), largest Lyapunov exponent (LLE) and correlation dimension (CD). All the RI and RE time series exhibit chaotic behavior. Specific coupling patterns were displayed in each ventilatory mode, and these patterns exhibited different linear and chaotic dynamics. When switching from ACV to IPS, partial inspiratory loading decreases the noise limit value, the LLE, and the correlation dimension of the RI and RE time series in parallel, whereas decreasing intrathoracic pressure from IPS to USB has the opposite effect. Coupling with expiration exhibits higher complexity than coupling with inspiration during mechanical ventilation either during ACV or IPS, probably due to active expiration. Only 33% of the cardiac time series (RR interval) exhibit complexity either during ACV, IPS, or USB making the contribution of the cardiac signal to the chaotic feature of the coupling minimal. We conclude that 1) CVC in unsedated humans exhibits a complex dynamic that can be chaotic, and 2) ventilatory mode has major effects on the linear and chaotic features of the coupling. Taken together these findings reinforce the role of ventilation in the CVC process.

scholarly journals A Search for Chaotic Behavior in Northern Hemisphere Stratospheric Variability

2014 ◽  
Vol 71 (4) ◽  
pp. 1494-1507 ◽  
Author(s):  
Gualtiero Badin ◽  
Daniela I. V. Domeisen
Keyword(s):  
Time Series ◽  
Numerical Model ◽  
Northern Hemisphere ◽  
Gaussian Distribution ◽  
Chaotic Attractor ◽  
Correlation Dimension ◽  
Chaotic Behavior ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
Stratospheric Variability

Abstract Northern Hemisphere stratospheric variability is investigated with respect to chaotic behavior using time series from three different variables extracted from four different reanalysis products and two numerical model runs with different forcing. The time series show red spectra at all frequencies and the probability distribution functions show persistent deviations from a Gaussian distribution. An exception is given by the numerical model forced with perpetual winter conditions—a case that shows more variability and follows a Gaussian distribution, suggesting that the deviation from Gaussianity found in the observations is due to the transition between summer and winter variability. To search for the presence of a chaotic attractor the correlation dimension and entropy, the Lyapunov spectrum, and the associated Kaplan–Yorke dimension are estimated. A finite value of the dimensions can be computed for each variable and data product, with the correlation dimension ranging between 3.0 and 4.0 and the Kaplan–Yorke dimension between 3.3 and 5.5. The correlation entropy varies between 0.6 and 1.1. The model runs show similar values for the correlation and Lyapunov dimensions for both the seasonally forced run and the perpetual-winter run, suggesting that the structure of a possible chaotic attractor is not determined by the seasonality in the forcing, but must be given by other mechanisms.

ESTIMATING CORRELATION EXPONENTS OF THE HEARTBEAT TIME SERIES

2000 ◽  
Vol 10 (06) ◽  
pp. 1513-1520 ◽  
Author(s):  
CAMILLO CAMMAROTA
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Stochastic Processes ◽  
Correlation Dimension ◽  
Mixing Properties ◽  
Correlation Exponent ◽  
Difference Series ◽  
The Difference

The heartbeat time series commonly used in diagnostics is investigated. Since this series is not stationary, the difference series is considered and in the framework of stochastic processes its stationarity and mixing properties are tested. For this kind of data, affected by noise and low precision, a notion of correlation exponent, in some sense related to the correlation dimension, is proposed. The data analysis shows the existence of a profile of the correlation exponents, which evidentiates the amounts of randomness and of determinism in the heartbeat dynamics.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

scholarly journals Assessing Stream-Aquifer Connectivity in a Coastal California Watershed

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 416
Author(s):  
Bwalya Malama ◽  
Devin Pritchard-Peterson ◽  
John J. Jasbinsek ◽  
Christopher Surfleet
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Water Level ◽  
Time Series Data ◽  
Series Data ◽  
Low Permeability ◽  
Pumping Tests ◽  
Stream Flows ◽  
The Impact

We report the results of field and laboratory investigations of stream-aquifer interactions in a watershed along the California coast to assess the impact of groundwater pumping for irrigation on stream flows. The methods used include subsurface sediment sampling using direct-push drilling, laboratory permeability and particle size analyses of sediment, piezometer installation and instrumentation, stream discharge and stage monitoring, pumping tests for aquifer characterization, resistivity surveys, and long-term passive monitoring of stream stage and groundwater levels. Spectral analysis of long-term water level data was used to assess correlation between stream and groundwater level time series data. The investigations revealed the presence of a thin low permeability silt-clay aquitard unit between the main aquifer and the stream. This suggested a three layer conceptual model of the subsurface comprising unconfined and confined aquifers separated by an aquitard layer. This was broadly confirmed by resistivity surveys and pumping tests, the latter of which indicated the occurrence of leakage across the aquitard. The aquitard was determined to be 2–3 orders of magnitude less permeable than the aquifer, which is indicative of weak stream-aquifer connectivity and was confirmed by spectral analysis of stream-aquifer water level time series. The results illustrate the importance of site-specific investigations and suggest that even in systems where the stream is not in direct hydraulic contact with the producing aquifer, long-term stream depletion can occur due to leakage across low permeability units. This has implications for management of stream flows, groundwater abstraction, and water resources management during prolonged periods of drought.

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