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1

Investigation of alterations in droughts and floods patterns induced by climate change

Rahmani Farhang, Fattahi Mohammad Hadi

Acta Geophysica

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2024

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Vol. 72, no. 1

405--418

EN

Every year, droughts and floods cause significant damage to the economy and water resources of the UK. Numerous studies have been explored droughts and floods from various points of view, however few have pointed the variations in the patterns induced by climate change. The precipitation data of Central England in the UK was gathered from 1931 to 2020. The analysis was performed by application of fractal dimension, noise variance, Lyapunov exponent, approximate entropy, extreme climate indices, and Standard Precipitation Index. The cross-correlation results indicated the study area warming owing to CO2 emissions on a global and local scale, implicating the climate change in the study area. Moreover, the mean maximum and minimum temperatures were affected by CO2 emissions on global and local scales, respectively. The nonlinear dynamic analysis indicated that the duration and intensity of the dry and wet spells were increased due to climate change. In other words, the droughts’ intensity and duration were augmented. However, the number of annual droughts and wetness’s have remained unaffected by climate change. The results signified a weakening in the flash floods possibility and an increment in the flash floods severity owing to climate change. Moreover, climate change brought about an intensification in the rivers’ inundation (fluvial floods) probability. The findings of the present study contribute to the understanding of the mechanism of climate change impacts on droughts and floods (flash, pluvial, and fluvial) patterns and furnished references for nonlinear dynamic studies of droughts and floods patterns.

2

DCNN oscillator design, implementation, and performance evaluation

Salih Thair A., Mohammed Emad A., Abdal Yasir M.

Przegląd Elektrotechniczny

|

2023

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R. 99, nr 4

84--88

EN

FPAAs technology are the ideal solution for creating an analog system. FPAA describes and implements the architecture of a simple CNN model used to build a delayed cellular neural network (DCNN) oscillator in this letter. Matlab simulation was carried out in order to analyze the proposed system. The attraction spectrum with different initial conditions, as well as Lyapunov's motives, were used to investigate the fundamental characteristics of the proposed system. The effect of noise on the proposed system was investigated. The promising results obtained encourage the application of the proposed model in secure communication systems.

PL

Technologia FPAA jest idealnym rozwiązaniem do stworzenia systemu analogowego. W tym liście FPAA opisuje i implementuje architekturę prostego modelu CNN używanego do budowy oscylatora opóźnionej komórkowej sieci neuronowej (DCNN). W celu analizy proponowanego systemu przeprowadzono symulację w Matlabie. Widmo przyciągania z różnymi warunkami początkowymi, a także motywy Lapunowa zostały wykorzystane do zbadania podstawowych cech proponowanego systemu. Zbadano wpływ hałasu na proponowany system. Uzyskane obiecujące wyniki zachęcają do zastosowania proponowanego modelu w bezpiecznych systemach komunikacyjnych.

3

Dynamical properties of a modified chaotic Colpitts oscillator with triangular wave non-linearity

Suresh Rasappan, Sathish Kumar Kumaravel, Regan Murugesan, Niranjan Kumar K. A., Narmada Devi R., Obaid Ahmed J.

Archives of Control Sciences

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2023

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Vol. 33, No. 1

25--53

EN

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced for triangular wave non-linearity. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.

4

Using nonlinear measures to evaluate postural control in healthy adults during bipedal standing on an unstable surface

Kędziorek Justyna, Błażkiewicz Michalina, Kaczmarczyk Katarzyna

Acta of Bioengineering and Biomechanics

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2022

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Vol. 24, no. 1

9--17

EN

This study examined the use of nonlinear measures – sample entropy (SampEn), fractal dimension (FD), and the Lyapunov exponent (LyE) – to evaluate postural control in adults during standing on an unstable surface, with and without visual feedback. Methods: 14 healthy young adults (24.07 ± 7.32 years) completed bipedal standing trials on an unstable-plate Biodex Balance System (BBS) connected to a Vicon system, with eyes open and closed. Each trial lasted 20 sec. Analysis was performed based on the center of mass (CoM), for which the three nonlinear measures were calculated. Results: Excluding visual feedback was found to cause a significant increase in linear and nonlinear parameters. Moreover, SampEn and FD values were found to be significantly higher in the PD direction, compared to AP or ML, whereas LyE values in this direction were minimal. Conclusions: Results show that the three nonlinear measures provide a useful way of evaluating postural control in healthy adults. Moreover, it seems that introducing an unstable surface meant that the projection of the CoM was not perpendicular to the surface, but rather set at a certain continually changing angle, forcing the whole system to adapt to chaotic and unpredictable conditions. Such refined changes in conditions can be evaluated in a precise way only by using nonlinear measures.

5

Dynamics, control, stability, diffusion and synchronization of modified chaotic Colpitts oscillator

Rasappan Suresh, Niranjan Kumar K. A.

Archives of Control Sciences

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2021

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Vol. 31, No. 3

731--759

EN

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.

6

A robust method for early diagnosis of autism spectrum disorder from EEG signals based on feature selection and DBSCAN method

Abdolzadegan Donya, Moattar Mohammad Hossein, Ghoshuni Majid

Biocybernetics and Biomedical Engineering

|

2020

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Vol. 40, no. 1

482--493

EN

Electroencephalogram (EEG) is one of the most important signals for diagnosis of Autism Spectrum Disorder (ASD). There are different challenges such as feature selection and the existence of artifacts in EEG signals. This article aims to present a robust method for early diagnosis of ASD from EEG signal. The study population consists of 34 children with ASD between 3–12 years and 11 healthy children in the same ranges of age. The proposed approach uses linear and nonlinear features such as Power Spectrum, Wavelet Transform, Fast Fourier Transform (FFT), Fractal Dimension, Correlation Dimension, Lyapunov Exponent, Entropy, Detrended Fluctuation Analysis and Synchronization Likelihood for describing the EEG signal. In addition Density Based Clustering is utilized for artifact removal and robustness. Besides, features selection is applied based on different criterions such as Mutual Information (MI), Information Gain (IG), Minimum-Redundancy Maximum-Relevancy (mRmR) and Genetic Algorithm (GA). Finally, the K-Nearest-Neighbor (KNN) and Support Vector Machines (SVM) classifiers are used for final decision. As a result, the investigation indicates that the classification accuracy of the approach using SVM is 90.57% while for KNN it is 72.77%. Moreover, the sensitivity of the proposed method is 99.91% for SVM and 91.96% for KNN. Also, experiments show that DFA, LE, Entropy and SL features have considerable influence in promoting the classification accuracy.

7

A Novel Chaotic System and its Modified Compound Synchronization

Sun Junwei, Li Nan, Wang Yanfeng, Wang Wei

Fundamenta Informaticae

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2019

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Vol. 164, nr 2-3

259--275

EN

In this paper, a new chaotic system is proposed, whose dynamical behaviors are discussed with the change of the parameters in detail. The specific effects of different parameters on the system are also discussed. By adjusting these parameters of the proposed circuit, this nonlinear circuit can produce the different dynamical behaviors, such as, hyper chaotic behavior, periodic behavior, transient behavior, etc. Furthermore, a novel kind of modified compound synchronization has been investigated, where the multiple chaotic systems have been considered for different combination modes: the compound system of four scaling drive systems and one response system. The corresponding controllers are designed to realize the modified compound synchronization. The theoretical proofs and numerical simulations are given to demonstrate the validity and applicability of the proposed chaotic system and the modified compound synchronization.

8

Wybrane aspekty analizy danych pomiarowych złożonego systemu energetycznego pod kątem zachowań chaotycznych

Jankowski P.

Zeszyty Naukowe Akademii Morskiej w Gdyni

|

2018

|

nr 103

107--119

PL

W artykule przedstawiono przykład zachowania chaotycznego w wybranym fragmencie sieci elektroenergetycznej zamodelowanej nieliniowym układem równań różniczkowych. Artykuł omawia najistotniejsze aspekty identyfikacji zachowań chaotycznych w systemie na podstawie zarejestrowanego przebiegu czasowego tylko jednej zmiennej stanu bez znajomości wymiaru rzeczywistej przestrzeni fazowej.

EN

The article presents an example of chaotic behavior in a selected piece of the power network modeled by nonlinear system of differential equations. This article also discusses the most important aspects of identifying chaotic behavior in a system, based on only the recorded time course of one state variable without knowing the real dimension of the phase space.

9

Badanie przydatności procedur Rosensteina i Eckmanna do identyfikacji chaotycznych szeregów czasowych

Hallmann D., Jankowski P.

Zeszyty Naukowe Akademii Morskiej w Gdyni

|

2018

|

nr 103

120--136

PL

Artykuł przedstawia wyniki badań symulacyjnych z użyciem procedur Eckmanna i Rosensteina wyznaczających wykładniki Lapunowa na podstawie szeregu czasowego. Dla weryfikacji i oceny przydatności tych procedur, jako wzorcowy szereg czasowy wykorzystano punkty generowane przez odwzorowanie logistyczne, dla którego znana jest trajektoria współczynników Lapunowa.

EN

This paper presents the results of simulation tests using the Eckmann and Rosenstein procedures for calculating Lyapunov exponents based on a time series. For verifying and evaluating the suitability of these procedures as a reference time series, points generated by logistic mapping for which the trajectory of Lyapunov's coefficients is known was applied.

10

Ergodic Isoenergetic Molecular Dynamics for Microcanonical-Ensemble Averages

Hoover W. G., Hoover C. G.

Computational Methods in Science and Technology

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2018

|

Vol. 24, No. 2

155--158

EN

Considerable research has led to ergodic isothermal dynamics which can replicate Gibbs’ canonical distribution for simple (small) dynamical problems. Adding one or two thermostat forces to the Hamiltonian motion equations can give an ergodic isothermal dynamics to a harmonic oscillator, to a quartic oscillator, and even to the “Mexican-Hat” (doublewell) potential problem. We consider here a time-reversible dynamical approach to Gibbs’ “microcanonical” (isoenergetic) distribution for simple systems. To enable isoenergetic ergodicity we add occasional random rotations to the velocities. This idea conserves energy exactly and can be made to cover the entire energy shell with an ergodic dynamics. We entirely avoid the Poincaré-section holes and island chains typical of Hamiltonian chaos. We illustrate this idea for the simplest possible two-dimensional example, a single particle moving in a periodic square-lattice array of scatterers, the “cell model”.

11

Erbium-doped fiber ring laser dynamical analysis for chaos message masking scheme

Ali S. Z., Islam M. K.

Optica Applicata

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2017

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Vol. 47, nr 3

395--410

EN

A detailed dynamical analysis of erbium-doped fiber ring laser cavity loss configuration for the chaos message masking scheme is carried out to optimize the generation of high quality chaos. A threefold increase in Lyapunov exponent implying higher security, and a significant increase in chaos bandwidth is achieved, both ideal for secure optical communication and nonlinear chaotic applications. The pulsed chaos is chaotic in a pulse time interval in addition to the amplitude resulting in better concealment of data pulses in a time domain. The chaos spectrum is a flat broadband and rich in spikes making spectral detection of a message more difficult. The range of five key parameters for which erbium-doped fiber ring laser retains its chaotic behaviour is also increased significantly reducing the effectiveness of a brute force attack to guess the erbium-doped fiber ring laser parameters. The chaos message masking scheme provides a higher security in comparison with additive chaos modulation scheme for implementation of chaotic optical communication using erbium- doped fiber ring laser. The security of a complete end-to-end chaotic optical communication system is tested by launching a spectral attack to estimate the message signal. The message signal clearly hides in a stronger chaotic signal and its spectral contents are not discernible.

12

Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

Tacha O. I., Volos C. K., Stouboulos I. N., Kyprianidis I. M.

Archives of Control Sciences

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2016

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Vol. 26, no. 1

95--115

EN

In this paper a novel 3-D nonlinear finance chaotic system consisting of two nonlinearities with negative saving term, which is called ‘dissaving’ is presented. The dynamical analysis of the proposed system confirms its complex dynamic behavior, which is studied by using wellknown simulation tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents and phase portraits. Also, some interesting phenomena related with nonlinear theory are observed, such as route to chaos through a period doubling sequence and crisis phenomena. In addition, an interesting scheme of adaptive control of finance system’s behavior is presented. Furthermore, the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model.

13

Efficiency analysis of control algorithms in spatially distributed systems with chaotic behavior

Korus Ł.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 4

759--770

EN

The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms in spatially distributed systems like CMLs. This comparison is made based on qualitative and quantitative evaluation methods proposed in the previous paper such as the indirect Lyapunov method, Lyapunov exponents and the net direction phase indicator. As a summary of this paper, some conclusions which can be useful for creating a more efficient algorithm of controlling chaos in spatially distributed systems are made.

14

Quantification of stability in an agility drill using linear and nonlinear measures of variability

Mehdizadeh S., Arshi A. R., Davids K.

Acta of Bioengineering and Biomechanics

|

2014

|

Vol. 16, no. 3

59--67

EN

This study implemented linear and nonlinear methods of measuring variability to determine differences in stability of two groups of skilled (n=10) and unskilled (n=10) participants performing 3m forward/backward shuttle agility drill. We also determined whether stability measures differed between the forward and backward segments of the drill. Finally, we sought to investigate whether local dynamic stability, measured using largest finite-time Lyapunov exponents, changed from distal to proximal lower extremity segments. Three-dimensional coordinates of five lower extremity markers data were recorded. Results revealed that the Lyapunov exponents were lower (P<0.05) for skilled participants at all joint markers indicative of higher levels of local dynamic stability. Additionally, stability of motion did not differ between forward and backward segments of the drill (P>0.05), signifying that almost the same control strategy was used in forward and backward directions by all participants, regardless of skill level. Furthermore, local dynamic stability increased from distal to proximal joints (P<0.05) indicating that stability of proximal segments are prioritized by the neuromuscular control system. Finally, skilled participants displayed greater foot placement standard deviation values (P<0.05), indicative of adaptation to task constraints. The results of this study provide new methods for sport scientists, coaches to characterize stability in agility drill performance.

15

O regularności ciągłych układów

Szyda A.

Pomiary Automatyka Kontrola

|

2012

|

R. 58, nr 1

133-135

PL

W pracy rozważano zagadnienia regularności ciągłego układu liniowego z niestacjonarną macierzą stanu A(t). Przedstawiono formalną definicję układów regularnych, ich własności - wpływ na stabilność czy wykładniki Lapunowa. W artykule poszukiwane były warunki, dla których liniowy układ ciągły o przedziałami stałych współczynnikach będzie układem regularnym. Jednym z warunków regularności badanych układów jest komutowanie macierzy układu oraz zapewnienie istnienia granicy średniego czasu przebywania układu w danym stanie.

EN

In this paper there is considered the problem of regularity of continuous linear systems with a nonstationary state matrix on example of systems with piecewise constant coefficients. In Section 2 there is presented a formal definition of regular systems [3], necessities theorems and basic concepts. The properties of regular systems [4, 5] - impact on the stability and Lyapunov exponents are described in Section 3. Section 4 gives the conditions under which a continuous linear system with piecewise constant coefficients is a regular system. One of the conditions is that the state matrices should commute. The second condition is to ensure the existence of a limit of the average time of being in a given state (Fig. 1). The considerations in this paper are useful for understanding the nonstationary systems with constant coefficients. The study provided a proof under what as-sumptions and conditions a continuous linear system with piecewise constant coefficients is a regular system. The properties of regular systems: continuous dependence of the Lapunov exponents on coefficients, resistance to low noise and the fact that the Lyapunov exponents are sharp are important. These considerations can be applied to mathematical modelling and systems design.

16

Ekonometryczna analiza fraktalnych właściwości struktury przepływu gazu w wybranych stacjach I stopnia

Gurgul H., Suder M.

AGH Managerial Economics

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2012

|

nr 11

77-99

PL

W artykule przedstawiono wyniki badań nad identyfikacją struktur nieliniowych oraz chaosu deterministycznego występujących w procesach przepływu gazu w wybranych stacjach I stopnia z województw małopolskiego i podkarpackiego. Wykorzystując popularne metody statystyczne wykrywania chaosu, wykazano na przykładach szeregów czasowych z okresu od stycznia 2007 do września 2011 opisujących przepływy gazu na stacjach Solec-Zdrój, Czechówka, Miłocin, Głogów oraz Huta Sendzimira, że w badanych szeregach mogą występować struktury nieliniowe. Jednakże uzyskane wstępne wyniki wymagają dalszych badań i analiz, z wykorzystaniem danych pochodzących z innych stacji, a także bardziej zaawansowanych metod badawczych w celu pełnego potwierdzenia diagnozy odnośnie do chaotycznej struktury wielkości przepływu gazu na stacjach I stopnia.

EN

This paper presents results of research focused on identification of nonlinear structures and deterministic chaos which take place in gas flows in provinces Małopolska and Podkarpackie. Taking into account time series of gas flows at stations Solec Zdrój, Czechówka, Miłocin, Głogów and Huta Sendzimira from time period between January 2007 and September 2011, the authors detected by mean of respective identifications methods the existence of nonlinear structures in these time series. However the results are not unique. Therefore, the preliminary results should be checked in further research on the basis of other stations located in other provinces of Poland and by mean of more advance methods. These future research should definitely confirm or reject the existence of chaotic structure of gas flows at the stations of first order.

17

Stabilność ciągłych układów liniowych o zmiennych skokowo współczynnikach

Bal-Szyda A.

Przegląd Elektrotechniczny

|

2009

|

R. 85, nr 7

211-214

PL

W pracy przedstawiono problem wyznaczenia stabilności dla ciągłych układów liniowych o zmiennych współczynnikach w czasie, gdzie funkcja przełączająca jest przedziałami stała. Rozpatrywane były układy jedno (opisane skalarami) i wielowymiarowe (opisane przez macierze) niestacjonarne, dla tych układów wyznaczone zostały warunki stabilności za pomocą wykładników Lapunowa, normy macierzowej, wartości własnych oraz promienia spektralnego. Wyprowadzone warunki posłużyły do określenia asymptotycznej stabilności liniowych układów ciągłych o zmiennych skokowo współczynnikach.

EN

In this paper stability problem for continuous time-varying linear systems with piecewise constant switching signal is presented. Onedimensional - described by scalar (multidimensional - described by matrices) notstationary systems are consider, for such systems the stability conditions are proposed with the aid of Lapunov exponent, matrix norm, eigenvalues and spectral radius. Derived stability conditions are very useful for describing asymptotic stability of linear time-varying systems with continuous time.

18

Modeling of the friction process in a frictional pair of vehicle disc brake using phase space

Polak A., Oleksowicz S.

Problemy Eksploatacji

|

2009

|

nr 2

7-17

EN

The paper presents the possibility of applying selected topological tools in the process of the modeling, diagnosing, and monitoring of a friction pair. The paper includes a presentation of the parameters describing the working conditions of a frictional pair in the phase space (PS), which permits the elimination of the time component from the data in the form of a time series, which enables the analysis of non-linear periodic behaviours of the phase point. The trace of the trajectory of the phase point presents the character of the process concerned. This information is unavailable in the traditional analysis preceded by a process of the preparation of experimental data (statistical processes). Interpretation of the oscillation of the system is possible by using a graphic presentation of the results in the phase space. Such a manner of analysing the parameters of the operation of a frictional pair enables the prediction of the condition of the system in a short period of time.

PL

Artykuł przedstawia możliwość zastosowania wybranych narzędzi topologii matematycznej w procesie modelowania, diagnostyki oraz monitoringu pary ciernej. Przedstawienie parametrów opisujących stan pracy pary trącej w przestrzeni fazowej prowadzi do eliminacji składowej czasowej z rozpatrywanego szeregu czasowego danych wejściowych, co pozwala na analizę nieliniowych, okresowych zachowań punktu fazowego. Droga trajektorii punktu fazowego przedstawia charakter procesu tarcia. Informacja ta jest niedostępna w tradycyjnej analizie danych, poprzedzonej wstępną obróbką danych (procesy statystyczne). Interpretacja oscylacji generowanych przez system jest możliwa za pomocą graficznej prezentacji wyników w przestrzeni fazowej oraz parametrów opisujących zachowanie trajektorii punktu fazowego.

19

Asymptotic behavior of ultimately contractive iterated random Lipschitz functions

Alsmeyer G., Hölker G.

Probability and Mathematical Statistics

|

2009

|

Vol. 29, Fasc. 2

321--336

EN

Let (Fn)n≥0 be a random sequence of i.i.d. global Lipschitz functions on a complete separable metric space (X; d) with Lipschit constants L1; L2; : : : For n ≥0, denote by Mx n = Fn○ : : : ○ F1(x) and ^Mx n = Fn○ : : : ○ F1(x) the associated sequences of forward and backward iterations, respectively. If E log+ L1 < 0 (mean contraction) and E log+ d ( F1(x0); x0) is finite for some x0ЄX, then it is known (see [9]) that, for each x Є X, the Markov chain Mx n converges weakly to its unique stationary distribution π, while ^M xn is a.s. convergent to a random variable ^M∞ which does not depend on x and has distribution π. In [2], renewal theoretic methods have been successfully employed to provide convergence rate results for ^M x n, which then also lead to corresponding assertions for Mx n via Mx n d= ^M x n for all n and x, where d= means equality in law. Here our purpose is to demonstrate how these methods are extended to the more general situation where only ultimate contraction, i.e. an a.s. negative Lyapunov exponent limn→∞ n−1 log l(Fn○ : : : ○ F1) is assumed (here l(F) denotes the Lipschitz constant of F). This not only leads to an extension of the results from [2] but in fact also to improvements of the obtained convergence rate.

20

Lyapunov exponent of the optical radiation scattered by the Brownian particles

Gavrylyak M. S., Maksimyak O. P., Maksimyak P. P.

Optica Applicata

|

2008

|

Vol. 38, nr 3

539-548

EN

The computer and physical simulation of light scattering by the system of Brownian particles has been carried out. Temporary fluctuations of field intensity have been found to save chaotic properties of driving particles. Empirical diagnostic links have been retrieved of the largest Lyapunov exponent of fluctuations of field intensity with parameters of the dispersive media.