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Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Purpose. To provide a procedure for identifying chaotic processes in a dynamic system and to examine time series, describing the chemical composition of cast iron at the blast furnace output with the purpose of identifying the nonlinearity of the investigated system and detecting the presence of chaotic processes in it. Methodology. The determination of the unique characteristics of the attractor of a dynamic chaotic system based on the time series of cast iron’s chemical composition values was carried out using methods of nonlinear dynamics and dynamic chaos theory, such as the autocorrelation function method, correlation and fractal dimensions. Findings. The methods of nonlinear dynamics and dynamic chaos theory were used to study the behavior of time series data on the chemical composition of cast iron at the blast furnace output. The presence was identified of chaotic processes with a fractal structure in the studied dynamic system, leading to the inefficiency of traditional analysis methods based on the Gaussian properties of stochastic processes. Originality. For the first time, the possibility and feasibility of applying chaos theory methods for the analysis and prediction of time series data on the chemical composition of cast iron at the blast furnace output were substantiated. For the first time, the nonlinearity of the studied dynamic system was identified, and chaotic processes were discovered within it by determining the unique characteristics of the strange attractor of the system using the analyzed time series, such as embedding dimension, time delay, and the largest Lyapunov exponent. Practical value. The obtained results open up the possibility for more effective and qualitative analysis of the behavior of the studied dynamic system by developing new tools for assessment and prediction that are adequate to the nature of the ongoing processes. [ABSTRACT FROM AUTHOR]

Chaos identification can not only promote the development and perfection of chaos theory, but also help to find the factors that produce chaos in the considered system, and control or anti-control it. The 0–1 test for chaos is an effective method to detect chaos. In order to simulate the noise contaminated through its production, Gaussian, Exponential, and Uniform noises are added to Logistic mapping to form a new hybrid time series, respectively. The effects of noise types and levels on the modified 0–1 test for chaos are studied. By studying the effect of different types of noises on chaos index D c ∗ (n) , K corr ∗ (c) , and the change of K m.corr ∗ (c) with amplitude α , it can be seen that Uniform noise has the greatest effect on chaos identification. In addition, it is found that the effect of the noise types on chaos identification depends on the peak of the noisy time series, and the effect of the noise on chaos detection increases with the increase of the noisy time series peak. It is worth noting that the selection of amplitude α can improve the noise resistance of chaos identification. The noise resistance of the modified 0–1 test for chaos can be improved by adjusting the amplitude α of the parameters. With the continuous increase of noise contamination level, the effect on the modified 0–1 test for chaos detection results is gradually enhanced, so reducing the noise contamination level is the key to improving the accuracy of the modified 0–1 test for chaos. In addition, adjusting the amplitude α can also play a certain noise immunity effect, and when α = 2 , the noise immunity is stronger on logistic mapping. Sample size N up to 2 0 0 0 is sufficient, but amplitude ω has little effect on chaos identification. [ABSTRACT FROM AUTHOR]

Physiological phenomena exhibit complex behaviours arising at multiple time scales. To investigate them, techniques derived from chaos theory were applied to physiological signals, providing promising results in distinguishing between healthy and pathological states. Fractal-like properties of electrodermal activity (EDA), a well-validated tool for monitoring the autonomic nervous system state, have been reported in previous literature. This study proposes the multiscale complexity index of electrodermal activity ( M C o m E D A ) to discern different autonomic responses based on EDA signals. This method builds upon our previously proposed algorithm, C o m E D A , and it is empowered with a coarse-graining procedure to provide a view at multiple time scales of the EDA response. We tested M C o m E D A 's performance on the EDA signals of two publicly available datasets, i.e., the Continuously Annotated Signals of Emotion (CASE) dataset and the Affect, Personality and Mood Research on Individuals and Groups (AMIGOS) dataset, both containing physiological data recorded from healthy participants during the view of ultra-short emotional video clips. Our results highlighted that the values of M C o m E D A were significantly different (p-value < 0.05 after Wilcoxon signed rank test with Bonferroni's correction) when comparing high- and low-arousal stimuli. Furthermore, M C o m E D A outperformed the single-scale approach in discriminating among different valence levels of high-arousal stimuli, e.g., showing significantly different values for scary and amusing stimuli (p-value = 0.024). These findings suggest that a multiscale approach to the nonlinear analysis of EDA signals can improve the information gathered on task-specific autonomic response, even when ultra-short time series are considered. [ABSTRACT FROM AUTHOR]

The short-term traffic flow prediction can help to reduce flight delays and optimize resource allocation. Using chaos dynamics theory to analyze the chaotic characteristics of en-route traffic flow is the basis of short-term en-route traffic flow prediction and ensuring the orderly and smooth state of the en-route. This paper takes the time series of en-route traffic flow extracted from Automatic-Dependent Surveillance Broadcast (ADS-B) measured data as the research object, uses the improved C–C method to reconstruct the phase space, and uses the improved small data volume method to calculate the Lyapunov index to identify the chaos phenomenon of en-route traffic flow. In order to avoid the interference of chaos phenomenon on traffic prediction, the Wavelet Neural Network (WNN) model is established to predict the traffic flow at en-route points. The experimental shows that when the number of iterations is 10,000, the average accuracy of WNN prediction is 0.87173, and the average running time is 6.9335334 s. According to the experimental results, it can be seen that the smaller number of iterations has more advantages in running time, which greatly reduces the overall running time. At the same time, it indicates that appropriately increasing or reducing the number of iterations in this experiment has little effect on the results. [ABSTRACT FROM AUTHOR]

Chaotic systems depict complex dynamics, thanks to their nonlinear behaviors. With recent studies on fractional-order nonlinear systems, it is deduced that fractional-order analysis of a chaotic system enriches its dynamic behavior. Therefore, the investigation of the chaotic behavior of a 4D memristive Chen system is aimed in this study by taking the order of the system as fractional. The nonlinear behavior of the system is observed numerically by comparing the fractional-order bifurcation diagrams and Lyapunov Exponents Spectra with 2D phase portraits. Based on these analyses, two different fractional orders (i.e., q = 0.948 and q = 0.97) are determined where the 4D memristive system shows chaotic behavior. Furthermore, a single state fractional-order sliding mode controller (FOSMC) is designed to maintain the states of the fractional-order memristive chaotic system on the equilibrium points. Then, control method results are obtained by both numerical simulations and different illustrative experiments of microcontroller-based realization. As expected, voltage outputs of the microcontroller-based realization are in good agreement with the time series of numerical simulations. [ABSTRACT FROM AUTHOR]

Copyright of Formación Universitaria is the property of Centro de Informacion Tecnologica (CIT) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We carry out an evolutionary study of the COVID-19 pandemic, focusing on the case of Lebanon. The disease spread exhibits four eruption phases or waves. Chaos theory tools point toward a correlation of events, essentially obeying a quasi-deterministic chaotic regime. The analysis of the time series yields a largest Lyapunov exponent of 0.263, indicative of a chaotic trend. The review of past and recent analyses and modeling of pandemics could assist in the predictabilty of their course of evolution, effective management and decision making for health authorities. [ABSTRACT FROM AUTHOR]

Chaotic systems have proven highly beneficial in engineering applications. Pseudo-random numbers produced by chaotic systems have been used for secure communication, notably image encryption. Specific characteristics can increase the chaotic behavior of the system by adding complexity and nonlinearity. The three most well-known characteristics are memristive properties, multistability (coexisting attractors), and hidden attractors. These characteristics strengthen the produced time series' unpredictability and randomness, strengthening an encryption algorithm's resistance to many attacks. This study introduces a unique four-dimensional chaotic system with extreme multistability with respect to three initial conditions (including the memristor initial condition) and all previously known properties. It is rare to find an extreme multistable system like this. This system is coupled with a quadratic flux-controlled memristor based on the well-known Sprott J system. This system has a line of unstable equilibrium points with hidden attractors. The memristor displays the characteristic pinched hysteresis loops, where the area inside a loop and the voltage frequency are inversely related. A comprehensive dynamical analysis thoroughly examines all system characteristics and initial conditions. The numerical findings are carefully verified, and an analog circuit is successfully built and simulated. The chaotic sequences generated by this system are combined with deoxyribonucleic acid (DNA) operations and the global bit scrambling (GBS) technique to create an image encryption algorithm that has strong resistance to a variety of potential attacks, including noise, statistical, exhaustive, differential, and cropping attacks. [ABSTRACT FROM AUTHOR]

Structural change tests aim to identify evidence of a structural break or change in the underlying generating process of a time series. The BDS test has its origins in chaos theory and seeks to test, using the correlation integral, the hypothesis that a time series is generated by an identically and independently distributed (IID) stochastic process over time. The BDS test is already widely used as a powerful tool for testing the hypothesis of white noise in the residuals of time series models. In this paper, we illustrate how the BDS test can be implemented also in a recursive manner to evaluate the hypothesis of structural change in a time series, taking advantage of its ability to test the IID hypothesis. We apply the BDS test repeatedly, starting with a sub-sample of the original time series and incrementally increasing the number of observations until it is applied to the full sample time series. A structural change in the unknown underlying generator model is detected when a change in the trend shown by this recursively computed BDS statistic is detected. The strength of this recursive BDS test lies in the fact that it does not require making any assumptions about the underlying time series generator model. We ilustrate the power and potential of this recursive BDS test through an application to real economic data. In this sense, we apply the test to assess the structural changes caused by the COVID-19 pandemic in international financial markets. Using daily data from the world's top stock indices, we have detected strong and statistically significant evidence of two major structural changes during the period from June 2018 to June 2022. The first occurred in March 2020, coinciding with the onset of economic restrictions in the main Western countries as a result of the pandemic. The second occurred towards the end of August 2020, with the end of the main economic restrictions and the beginning of a new post-pandemic economic scenario. This methodology to test for structural changes in a time series is easy to implement and can detect changes in any system or process behind the time series even when this generating system is not known, and without the need to specify or estimate any a priori generating model. In this sense, the recursive BDS test could be incorporated as an initial preliminary step to any exercise of time series modeling. If a structural change is detected in a time series, rather than estimating a single predictive model for the full-sample time series, efforts should be made to estimate different predictive models, one for the time before and one for the time after the detected structural change. [ABSTRACT FROM AUTHOR]

Time series of stock indices usually exhibit nonstationary and chaotic behavior. Analysis of the characteristics of the business cycle can reveal pertinent insights into the evolution of the stock volatility. This paper studies the characteristic periods of three main Chinese stock indices, i.e., the Shanghai composite index (SHCI), the Shenzhen component index (SZCI), and the Hang Seng index (HSI). We propose an approach based on the successive one-sided Hodrick-Prescott (SOHP) filtering and wavelet analysis of the empirical data from the stock markets, to detect their characteristic periods. In particular, the SOHP filter, which preprocesses the time series with a moving-horizon optimization procedure, enables us to extract the volatility cycles in different time scales from a stock time series and reduce noise distortion. The characteristic period of the stock index is then determined by the maxima of the wavelet power spectrum of the filtered data. The evolution of the characteristic period in time demonstrates rich information concerning the period stability of the stock market, as well as the cause and effect of the stock crash. To facilitate solving the moving-horizon optimization issue of the SOHP filter, we also present an incremental HP filtering algorithm, which greatly simplifies the involved inverse matrix operation in the HP-type filters. [ABSTRACT FROM AUTHOR]

Superspreading has become a key mechanism of COVID-19 transmission which creates chaos. The classical approach of compartmental models may not sufficiently reflect the epidemiological situation amid superspreading events (SSEs). We perform a data-driven approach and recognise the deterministic chaos of confirmed cases. The first derivative (≈ difference of total confirmed cases) and the second derivative (≈ difference of the first derivative) are used upon SSEs to showcase the chaos. Varying solution trajectories, sensitivity and numerical unpredictability are the chaotic characteristics discussed here. [ABSTRACT FROM AUTHOR]

General aviation accidents have complex interactions and influences within them that cannot be simply explained and predicted by linear models. This study is based on chaos theory and uses general aviation accident data to conduct research on different timescales (HM-scale, ET-scale, and EF-scale). First, time series are constructed by excluding seasonal patterns from the statistics of general aviation accidents. Secondly, the chaotic properties of multi-timescale series are determined by the 0–1 test and Lyapunov exponent. Finally, by introducing the sparrow search algorithm and tent chaotic mapping, a CSSA-LSSVM prediction model is proposed. The accident data of the National Transportation Safety Board (NTSB) of the United States in the past 15 years is selected for case analysis. The results show that the phase diagram of the 0–1 test presents Brownian motion characteristics, and the maximum Lyapunov exponents of the three scales are all positive, proving the chaotic characteristics of multi-timescale series. The CSSA-LSSVM prediction model's testing results illustrate its superiority in time series predicting, and when the timescale declines, the prediction error reduces gradually while the fitting effect strengthens and then decreases. This study uncovers the nonlinear chaotic features of general aviation accidents and demonstrates the significance of multi-timescale research in time series analysis and prediction. [ABSTRACT FROM AUTHOR]

Theoretically, an eight-term chaos system is presented. The effect of changing the initial conditions values on behavior Chen system was studied. The basic dynamical properties of system are analyzed like time series, attractor, FFT spectrum, and bifurcation. Where the system appears steady state behavior at initial condition xi, yi, zi equal (0, 0, 0) respectively and it convert to quasi-chaotic at xi,yi,zi equal (-0.1, 0.5,-0.6). Finally, the system become hyper chaotic at xi,yi, zi equal(- 0.5, 0.5,-0.6 ) that can used it in many applications like secure communication. [ABSTRACT FROM AUTHOR]

Chaos means innovation in the field of design. Meanwhile, the product image system is not only a quantified 'formula' between product and psychological cognitive semantics, but also a nonlinear "system". Therefore, the chaotic study of product color image system was carried out to grasp the users' color sensibility demands in their complex and nonlinear perceptual cognitive processes accurately, which could help the developers to keep up with market trends and reduce the blindness of design. In this study, the Chaos Theory combine with the Kansei Engineering were applied to obtain the color brand image, collect the time series and analyze the chaos of product color image system. The results showed that product color image system has a chaotic characteristic. Furthermore, the chaotic phenomenon in the color image system of the available products was analyzed to show that the product color trends could be quantitatively predicted. At last, a product color image perception chaotic box was proposed to conceive based on the result of this study, which provides new ideas and theoretical support for the in-depth exploration of complex systems of color images. This is a new attempt to apply the Chaos Theory to the color image cognition process. [ABSTRACT FROM AUTHOR]

Many researchers proved that hybrid models have better results in comparison with independent models. A combination of different methods could enhance the accuracy of time series prediction. Hence, this research used the hybrid of three methods of chaos theory, multi-layer perceptron and metaheuristic algorithm to increase the power of the model forecasting. Artificial neural networks have properly considered complex nonlinear relations and are good comprehensive approximators. Multi-objective evolutionary algorithms such as multi-objective particle swarm optimization are good at solving multi-objective optimization issues. This algorithm organized the combination of parent and children populations by elitist strategy, decreased the messy comparing factors to improve the solution variety and avoided to use of niche factors. Chaos theory controls the complexities of stochastic systems. So, this research offers Tehran Stock Exchange Index (TSEI) prediction by a hybrid model of chaos theory, multi-layer perceptron and metaheuristic algorithm. The results show that in perceptron-based mode, RMSE measures are gradually increased in all intervals. The continuous decrease of RMSE shows that the perceptron-based model could show consistency with the whole data flow. This matter could offer a better learning and consistency process by perceptron-based models to predict stock prices, as this type of learning could apply more experiences for forecasting future behaviour in order to change the system content. [ABSTRACT FROM AUTHOR]

Data-driven modeling methods have been widely used in many applications or studies of traffic systems with complexity and chaos. The empirical mode decomposition (EMD) family provides a lightweight analytical method for non-stationary and non-linear data. However, a large amount of traffic data in practice are usually multidimensional, so the EMD family cannot be used directly for those data. In this paper, a method to calculate the extremum point and the envelope-like function (series) from the complex function (series) is proposed so that the EMD family can be applied to two-variate traffic time-series data. Compared to the existing multivariate EMD, the proposed method has advantages in computational burden, flexibility and adaptivity. Two-dimensional trajectory data were used to test the method and its oscillatory characteristics were extracted. The decomposed feature can be used for data-driven traffic analysis and modeling. The proposed method also extends the utilization of EMD to multivariate traffic data for applications such as traffic data denoising, pattern recognition, traffic flow dynamic evaluation, traffic prediction, etc. [ABSTRACT FROM AUTHOR]

The economic burden of HIV extends beyond the individual level and affects communities and countries. HIV can lead to decreased economic growth due to lost productivity and increased healthcare costs. In some countries, the HIV epidemic has led to a reduction in life expectancy, which can impact the overall quality of life and economic prosperity. Therefore, it is significant to investigate the intricate dynamics of this viral infection to know how the virus interacts with the immune system. In the current research, we will formulate the dynamics of HIV infection in the host body to conceptualize the interaction of T-cells and the immune system. The recommended model of HIV infection is presented with the help of fractional calculus for more precious outcomes. We introduce numerical methods to demonstrate how the input parameters affect the output of the system. The dynamical behavior and chaotic nature of the system are visualized with the variation of different input factors. The system's tracking path has been numerically depicted and the impact of the viruses on T-cells has been demonstrated. In addition to this, the key factors of the system has been predicted through numerical findings. Our results predict that the strong non-linearity of the system is responsible for the chaos and oscillation, which are so closely related. The chaotic parameters of the system are highlighted and are recommended for the control of the chaos of the system. [ABSTRACT FROM AUTHOR]

Copyright of Iraqi Journal of Physics is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Detection of Stretching And Folding (SAF) traits in a time series is still controversial and of great interest. Also, visuo-manual tracking studies did not pay attention to SAF in hand motion trajectories. This research aims to find out the relevance of SAF to the discontinuities in chaotic dynamics of hand motion through target tracking tasks. Specifically, a new method is constructed based on this relation in which SAF can extract accurately trajectories in both time domain and phase space. Consequently, we designed experiments to track sinusoidal and trapezoidal target movements shown on a monitor. In these experiments, fourteen participants were instructed to move the joystick handle by wrist flexion-extension movements. Results confirm intermittency in significant human motor control behavior which results in discontinuities in hand motion trajectories. The relation between SAF and these discontinuities is realized by chaotic and intermittent behaviors of tracking dynamics. Verification of the method's accuracy is also carried out by taking advantage of the Poincaré section. Our method can provide insight into the dynamical behaviors of chaotic and intermittent systems involving mechanisms in human motor control. It can be applied to general systems with intermittent behavior and other systems with modification. [ABSTRACT FROM AUTHOR]

After an investigation of the well-known basic properties of muons conducted by the standard model (SM), this paper presents the results obtained for the phase space reconstruction, for the correlation dimension and for the largest Lyapunov exponent of a muon time series detected for a period of about three years (2019–2021) in an Italian laboratory at the sea level. These results confirm that the dynamics of such a time series is chaotic in nature, and therefore open new perspectives in the study of cosmic rays. In the following studies, we will explore if such muon time series have a mono- or a multifractal regime with a complete analysis of all the parameters that usually involve such studies. [ABSTRACT FROM AUTHOR]

Analytical methods derived from nonlinear dynamical systems, complexity, and chaos theories offer researchers a framework for in-depth analysis of time series data. However, relatively few studies involving time series data obtained from psychological and behavioral research employ such methods. This paucity of application is due to a lack of general analysis frameworks for modeling time series data with strong nonlinear components. In this article, we describe the potential of Hankel alternative view of Koopman (HAVOK) analysis for solving this issue. HAVOK analysis is a unified framework for nonlinear dynamical systems analysis of time series data. By utilizing HAVOK analysis, researchers may model nonlinear time series data in a linear framework while simultaneously reconstructing attractor manifolds and obtaining a secondary time series representing the amount of nonlinear forcing occurring in a system at any given time. We begin by showing the mathematical underpinnings of HAVOK analysis and then show example applications of HAVOK analysis for modeling time series data derived from real psychological and behavioral studies. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Railway Science & Engineering is the property of Journal of Railway Science & Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Accurate carbon price forecasting is of great significance to the operation of carbon financial markets. However, limited by the non-linearity and non-stationarity of the carbon price, the accurate and reliable predictions are difficult. To address the issue of applicability and accuracy, a novel carbon price hybrid model based on decomposition, entropy, and machine learning methods is proposed, named as CEEMDAN-PE-LSTM-RVM. Adopting the advanced structure (i.e., the prediction under classification), the proposed model owns reliable performance in face of the cases with different complexity. Furthermore, the relationship between the data feature and prediction accuracy is discussed to provide a benchmark for judging the reliability of the prediction, in which the chaos degree is introduced as a feature to characterize carbon price quantitatively. The performance of the proposed model is evaluated through historical data of four representative carbon prices. The results show that the average MAPE and RMSE of the proposed model achieve 1.7027 and 0.7993, respectively, which is significantly greater than others; the proposed model owns great robustness, which is less affected by the complexity of predicted objects. Thus, the proposed model provides a reliable tool for carbon financial markets. [ABSTRACT FROM AUTHOR]

Rotary kiln temperature forecasting plays a significant part of the automatic control of the sintering process. However, accurate forecasts are difficult owing to the complex nonlinear characteristics of rotary kiln temperature time series. With the development of chaos theory, the prediction accuracy is improved by analyzing the essential characteristics of time series. However, the existing prediction methods of chaotic time series cannot fully consider the local and global characteristics of time series at the same time. Therefore, in this study, the global recurrence plot (GRP)-based generative adversarial network (GAN) and the long short-term memory (LSTM) combination method, named GRP-lstmGAN, are proposed, which can effectively display important information about time scales. First, the data is subjected to a series of pre-processing operations, including data smoothing. Then, transforming one-dimensional time series into two-dimensional images by GRP makes full use of the global and local information of time series. Finally, the combination of LSTM and improves GAN models for temperature time series prediction. The experimental results show that our model is better than comparison models. [ABSTRACT FROM AUTHOR]

To understand the ability and limitations of convolutional neural networks to generate time series that mimic complex temporal signals, we trained a generative adversarial network consisting of convolutional networks to generate chaotic time series and used nonlinear time series analysis to evaluate the generated time series. A numerical measure of determinism and the Lyapunov exponent showed that the generated time series well reproduce the chaotic properties of the original time series. However, error distribution analyses showed that large errors appeared at a low but non-negligible rate. Such errors would not be expected if the distribution were assumed to be exponential. [ABSTRACT FROM AUTHOR]

Background Various epidemiological studies have focused on the adverse health outcomes of meteorological factors. However, there has been little research on the impact of humidex on allergic conjunctivitis, especially in child and adolescent populations. We aimed to explore the impact of humidex, a comprehensive index of relative humidity and temperature, on child and adolescent allergic conjunctivitis admissions. Methods Outpatient visit data for allergic conjunctivitis, meteorological factors and air pollutants in Shanghai for the 2017-2022 period were retrieved. For the purpose of analysing the nonlinear connection and lag impact between humidex and admissions for paediatric and adolescent allergic conjunctivitis, the distributed lag nonlinear model (DLNM) was fitted. Results A total of 147 090 cases were included in our cohort. We found a significantly nonlinear effect on humidex and allergic conjunctivitis. In the single-day lag pattern, the relative risks (RR) of allergic conjunctivitis were significant at lag 0 (RR = 1.08, 95% confidence interval (CI) = 1.05-1.11) to lag 2 (RR = 1.01, 95% CI = 1.00-1.01), lag 5 (RR = 1.01, 95% CI = 1.00-1.01) to lag 9 (RR = 1.01, 95% CI = 1.00-1.01), and lag 14 (RR = 1.02, 95% CI: 1.01-1.03). In the cumulative-lag day pattern, the RR of allergic conjunctivitis were significant at lag 0-0 (RR = 1.08, 95% CI = 1.05-1.11) to lag 0-14 (RR = 1.21, 95% CI = 1.13-1.28). We found that boys, children aged 7-17 years, and children in the warm season were more vulnerable to humidex. In addition, the highest attributable fraction (AF) and attributable number (AN) of humidex are at lag 0-14 (AF = 0.17, AN = 25 026). Conclusions Humidex exposure markedly increased the risk of allergic conjunctivitis, especially in highly high humidex. Appropriate public health management is needed for disease management and early intervention. [ABSTRACT FROM AUTHOR]

Copyright of China Rural Water & Hydropower is the property of China Rural Water & Hydropower Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The availability of the system is one of the main requirements of a multimedia-based e-health application that carries critical patient health information in the network environment. On the other hand, the Distributed Denial of Service (DDoS) attack is one of the most common attacks on the availability of computer networks which can be devastating for a healthcare system. Therefore, a countermeasure to this attack has to be performed in the early steps of the attack to protect the systems against its damages. Detection methods cannot support this and are only able to detect the attack after it happened. Thus, it is necessary to predict DDoS attacks according to the evidence which the attack makes in the network in the early steps of the attack. Therefore, Prediction approaches can reduce the cost of the attacks compared to detection approaches. In this paper, we propose a new method for prediction of DDoS attack based on Lyapunov Exponent Analysis and Echo State Network (LEAESN). In this method, the future traffic of the network is predicted using the Exponential Smoothing technique, then the time series of the prediction error is calculated based on the difference of this prediction and the observed traffic of the network. As shown in this paper, this time series is chaotic in the presence of attack traffics. To predict the DDoS attack, this time series is predicted using a Recurrent Neural Echo State Network (SCESN), and the attack is detected using Lyapunov exponent analysis on the predicted time series. For the evaluation of LEAESN, we test the method on the Darpa98 dataset which consists of a standard dataset for evaluation of intrusion detection systems. LEAESN has an appropriate ability to predict the DDoS attack. [ABSTRACT FROM AUTHOR]

In this work, an eight-term chaos system is presented. The effect of changing the initial conditions values on behavior Chen system was studied. The research provided a complete analysis of the system properties such as time series, attractor, FFT spectrum and bifurcation. Where the system appears steady state behavior at initial conditions xi, yi, zi that equal (0, 0, 0) respectively and it convert to quasi-chaotic at xi, yi, zi equal (− 0.1, 0.5, − 0.6). Finally, the system become hyper chaotic at xi, yi, zi equal (− 1, 0.5, − 0.6) that can used it in many applications like secure communication. [ABSTRACT FROM AUTHOR]

The financial market is a complex system with chaotic behavior that can lead to wild swings within the financial system. This can drive the system into a variety of interesting phenomenon such as phase transitions, bubbles, and crashes, and so on. Of interest in financial modelling is identifying the distribution and the stylized facts of a particular time series, as the distribution and stylized facts can determine if volatility is present, resulting in financial risk and contagion. Regression modelling has been used within this study as a methodology to identify the goodness-of-fit between the original and generated time series model, which serves as a criterion for model selection. Different time series modelling methods that include the common Box–Jenkins ARIMA, ARMA-GARCH type methods, the Geometric Brownian Motion type models and Tsallis entropy based models when data size permits, can use this methodology in model selection. Determining the time series distribution and stylized facts has utility, as the distribution allows for further modelling opportunities such as bivariate regression and copula modelling, apart from the usual forecasting. Determining the distribution and stylized facts also allows for the identification of the parameters that are used within a Geometric Brownian Motion forecasting model. This study has used the Carbon Emissions Futures price between the dates of 1 May 2012 and 1 May 2022, to highlight this application of regression modelling. [ABSTRACT FROM AUTHOR]

Copyright of China Rural Water & Hydropower is the property of China Rural Water & Hydropower Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The entropic chaos degree measures the chaos of a dynamical system as an information quantity in the framework of Information Dynamics and can be directly computed for any time series even if the dynamical system is unknown. A recent study introduced the extended entropic chaos degree, which attained the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. Moreover, an improved calculation formula for the extended entropic chaos degree was recently proposed to obtain appropriate numerical computation results for multidimensional chaotic maps. This study shows that all Lyapunov exponents of a chaotic map can be estimated to calculate the extended entropic chaos degree and proposes a computational algorithm for the extended entropic chaos degree; furthermore, this computational algorithm was applied to one and two-dimensional chaotic maps. The results indicate that the extended entropic chaos degree may be a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics. [ABSTRACT FROM AUTHOR]

We explore the influence and advantages of integrating chaotic systems with deep learning for time series forecasting in this paper. It proposes a novel deep learning method based on the Chen system, which leverages the randomness, sensitivity, and diversity of chaotic mapping to enhance the performance and efficiency of deep learning models. We introduce a deep learning framework that integrates chaotic systems, providing an innovative and effective approach for time series forecasting. The research utilizes three different types of deep learning models as baselines—Long Short-Term Memory, Neural Basis Expansion Analysis, and Transformer—and compares them with their chaotic counterparts to demonstrate the impact of chaotic systems on various deep learning architectures. Experimental validation is conducted on thirteen available time series datasets, assessing the models' forecasting accuracy, runtime, and resource occupancy. The effectiveness and superiority of the chaotic deep learning method are verified across diverse datasets, including stock markets, electricity, and air quality, showcasing significant improvements over traditional model initialization methods. • Chen system boosts deep learning for precise time series forecasting. • Chaotic models outperform traditional deep learning in accuracy and robustness. • Models save resources and adapt better across diverse datasets. • Promising results in finance, power systems, and weather forecasting. [ABSTRACT FROM AUTHOR]

This work explores the dynamic laws of electrical contact resistance (ECR) signals measured in the sliding current-carrying friction tests based on chaos theory. It is found that ECR time series have a chaotic nature, strongly verified by the positive largest Lyapunov exponent λ 1. The chaos may originate from the combined friction effects on short and long timescales. Phase space analysis indicates that the ECR phase trajectory adheres to the "convergence–stability" evolution law over time, which pertains closely to energy dissipation. Hence, the chaotic attractor exists during current-carrying friction. Strikingly, wear surfaces confirm that the ECR phase trajectory evolution process corresponds to the stages of "formation–keeping" of the chaotic attractor, and also agrees with the electrical wear stages of "running-in–steady-state". Further, the chaos quantifier variation is consistent with the phase space analysis results to identify wear transition quantitatively. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stochastic dynamics of a class of nonlinear ship rolling motion with multiplicative noise under both displacement and velocity delay feedback controls. The I t o ˆ -stochastic differential equation for the amplitude and phase of the roll motion is derived using the stochastic center manifold method and stochastic average method. Subsequently, the stochastic stability and bifurcation behaviors of the system are analyzed. Furthermore, using the stationary probability density method, we derive the parameter conditions for the occurrence of stochastic D -bifurcation and stochastic P -bifurcation. We also analyze the properties and shape changes of the system's probability density function under different parameters through numerical simulation. It has been determined that the system exhibits stochastic bifurcation behavior, specifically P -bifurcation and D -bifurcation. The validity of the method is verified by a numerical model. The theoretical chaos threshold of the system is determined using the random Melnikov method, and the impact of delayed feedback parameters on the chaotic motion of the system is analyzed by combining the bifurcation diagram, phase portrait, and time series. • We investigate the stochastic dynamics of a class of nonlinear ship rolling motion with multiplicative noise under both displacement and velocity delay feedback controls. • The Ito-stochastic differential equation for the amplitude and phase of the roll motion is derived using the stochastic center manifold method and stochastic average method. • Using the stationary probability density method, we derive the parameter conditions for the occurrence of stochastic D-bifurcation and stochastic P-bifurcation. • The theoretical chaos threshold is determined using the random Melnikov method. [ABSTRACT FROM AUTHOR]

Chaotic dynamics are abundantly present in nature as well as in manufactured devices. While chaos in some systems is an undesired phenomenon, in others, they are advantageous because of several applications. Therefore, there is an interest in developing accurate and robust tools for detecting chaos in systems. When the equations describing the system are known, the largest Lyapunov exponent method is used to classify regular from chaotic dynamics. However, when analyzing a process, it often happens that the exact form of the underlying equations is not known. Therefore, it is important to have tools allowing chaos detection using only the time series generated by the theoretical or experimental systems. In this paper, we propose an approach using the single nonlinear node delay-based reservoir computer to separate regular from chaotic dynamics. We show that its classification capabilities are robust with an accuracy of up to 99.03%. We also study the effect of the length of the time series N on the performance of our approach and demonstrate that high accuracy is achieved with short time series ( N ≥ 20 ). Moreover, we demonstrate that the reservoir computer trained with the standard map can classify the dynamical state of another system (for instance, the Lorenz system). [ABSTRACT FROM AUTHOR]

Micro Doppler phenomenon enables radars to study manifestations of micro movements on top of a moving body. Recent studies have successfully demonstrated the calibre of off body radar sensor nodes in human activity recognition, using time - frequency plots. In this paper, Recurrence Quantification Analysis(RQA) and Poincaré plot based features have been introduced for action classification using radars. Using the underlying idea that each action introduces a unique sequence of pattern in time frequency plots and subsequently Cadence Velocity Diagrams(CVD), we extract state distance matrix from CVD, considering each cadence frequency as a unique state. RQA statistics and Poincaré features try to encapsulate this uniqueness. Additionally, Recurrence plots are used to provide a novel way of representation of micro Doppler data. The signal processing pipeline is tested on experimental data collected from 9 subjects for 8 actions, providing testing accuracy on unseen data of 96.8%, thus demonstrating the efficacy of the proposed method. Average value for both precision and recall is 0.97. Standard deviation for precision and recall is 0.03 and 0.05 respectively. [ABSTRACT FROM AUTHOR]

In this paper, a novel combination of deep learning recurrent neural network and Lyapunov time is proposed to forecast the consumption of electricity load, in Greece, in normal/abrupt change value areas. Our method verifies the chaotic behavior of load time series through chaos time series analysis and with the application of deep learning recurrent neural networks produces predictions for 10 and 20 days ahead. Specifically, four different neural network models constructed (a) feed forward neural network, (b) gated recurrent unit (GRU) neural network, (c) long short-term memory (LSTM) recurrent and (d) bidirectional LSTM neural network to implement the prediction in a prediction horizon, produced through the extraction of maximum Lyapunov exponent. We constructed sequences of algorithms to feed the neural networks, creating three scenarios (a) 1-step, (b) 10-step and (c) 20-step sequences. For each neural network model, we used its predictions as inputs to predict steps forward, iteratively, to examine the accuracy of the proposed models, for horizons that are both inside and outside to that defined by Lyapunov time. The results show that the deep learning GRU neural network produces iterative predictions of high accuracy and stability, following the trend evolution of actual values, even outside the safe horizon for 1-step and 10-step cases. [ABSTRACT FROM AUTHOR]

Close encounters or resonances overlaps can create chaotic motion in small bodies in the Solar System. Approaches that measure the separation rate of trajectories that start infinitesimally near, or changes in the frequency power spectrum of time series, among others, can discover chaotic motion. In this paper, we introduce the ACF index (ACFI), which is based on the auto-correlation function of time series. Auto-correlation coefficients measure the correlation of a time-series with a lagged duplicate of itself. By counting the number of auto-correlation coefficients that are larger than 5% after a certain amount of time has passed, we can assess how the time series auto-correlates with each other. This allows for the detection of chaotic time-series characterized by low ACFI values. [ABSTRACT FROM AUTHOR]

Stock market prediction is extremely important for investors because knowing the future trend of stock prices will reduce the risk of investing capital for profit. Therefore, seeking an accurate, fast, and effective approach to identify the stock market movement is of great practical significance. This study proposes a novel turning point prediction method for the time series analysis of stock price. Through the chaos theory analysis and application, we put forward a new modeling approach for the nonlinear dynamic system. The turning indicator of time series is computed firstly; then, by applying the RVFL-GMDH model, we perform the turning point prediction of the stock price, which is based on the fractal characteristic of a strange attractor with an infinite self-similar structure. The experimental findings confirm the efficacy of the proposed procedure and have become successful for the intelligent decision support of the stock trading strategy. [ABSTRACT FROM AUTHOR]

Due to the existence of observation noise such as multi-path error, the accuracy of deformation prediction results are affected by using the data series of GNSS deformation monitoring. In order to examine the influence of measurement error on the deformation prediction results, the GNSS derived surface displacement time series of Miaodian landslide in Jingyang Area of Shaanxi, and those after noise suppression in combination with chaos theory were analyzed. Firstly, the mutual information method was used to determine the time delay of the surface displacement time series, and the Cao method was used to determine the embedding dimension to obtain the phase space reconstruction parameters. Secondly, the maximum Lyapunov exponent method was used to identify the chaotic characteristics of the two surface displacement time series. Finally, the weighted first-order local prediction method, the largest Lyapunov exponent prediction method, and the BP neural network prediction method were used to predict the landslide surface displacements. The results show that the GNSS landslide surface displacement time series and the time series after noise suppression have chaotic characteristics. The BP neural network prediction method has good prediction performance with an MAE of 0.4 mm and an MRE of 11.9%. After S-transform noise suppression, the MAE and MRE are 0.1 mm and 4.12%, respectively. Compared with the original time series, the prediction performance has been significantly improved after noise suppression. [ABSTRACT FROM AUTHOR]

Intensive and repetitive simulations are required to study static and dynamic behaviours of systems. Particular phenomena such as bifurcation and chaos require long simulation times and analysis. To check the existence of bifurcations and chaos in a dynamic system, a fine-tuning procedure of a bifurcation parameter is to be carried out. This increases considerably the computing time, and a great amount of patience is needed to obtain adequate results. Because of the high switching frequency of a boost inverter, the integration process of the dynamic model used to describe it uses an integration step that is in general less than one microsecond. This makes the integration process time consuming even for a short simulation. Thus, a fast, but accurate, method is suitable to analyse the dynamic behaviour of the converter. This work contains two topics. First, we develop a like-discrete integration process that permits precise results in a very fast manner. For one switching period, we compute only two or a maximum of three breaking points depending on whether we treat a continuous conduction mode (CCM) or a discontinuous conduction mode (DCM) of the inductor current. Furthermore, with each segment of the dynamic trajectory, an exact analytic formula is associated. The second goal is to use this result to develop a discrete iterative map formulated as in standard discrete time series models. The Jacobian matrix of the found iterative map is defined and used to compute Lyapunov exponents to prove existence of chaos. Performance of the developed study is positively evaluated by using classical simulations and fine-tuning a bifurcation parameter to detect chaos. This parameter is the desired reference of the inductor current peak. Results show that the proposed scheme is very fast and accurate. The study can be easily extended to other switching topologies of DC-DC inverters. [ABSTRACT FROM AUTHOR]

Many meteorological systems are chaotic in nature, which inevitably limits its predictability. Accurate prediction of meteorological variables depends primarily on properly diagnosing the complex underlying dynamics. Nonlinear dynamic analysis has shown to be particularly useful for such purpose. In this study, the concept of recurrence analysis was extended to investigate and characterize the underlying dynamics of meteorological time series (i.e., wind speed, temperature, pressure and relative humidity) based on daily observation in Hong Kong during a period from 1998 to 2018. The existence of chaos was clearly identified based on the phase space reconstruction diagram and the recurrence plot. It was shown that the underlying dynamics associated with wind speed appears to indicate higher level of complexity as compared to those of pressure and temperature, which, in consequence, may lead to more irregular time‐dependent behaviour and lower predictability. Moreover, season‐to‐seasonal variability in the dynamics of meteorological time series was evident, particularly for wind speed and temperature. Overall, this study shows that the recurrence analysis can be well applied as a useful diagnostic tool to investigate the dynamics of meteorological systems, which is expected to provide a new avenue regarding the modelling and prediction of the behaviour of meteorological parameters. [ABSTRACT FROM AUTHOR]

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