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IEEE International conference on Fuzzy Systems

作者： Tuan D. Pham Mayumi Oyama-Higa Department of Biomedical Engineering Linkoping University Linkoping Sweden Chaos Technology Research Laboratory Shiga Prefecture Japan

Photoplethysmogram (PPG) signals obtained from wearable sensors have been utilized for monitoring health conditions in both clinical and non-clinical environments, mostly concerning with heart-rate events. This paper shows the potential use of short-time PPG signals for differentiating patients with Parkinson's disease (PD) from healthy control (HC) subjects with nonlinear dynamics analysis. Multiscale entropy, time-shift multiscale entropy, and fuzzy recurrence plots were applied for extracting features from PPG signals of PD patients and HC subjects. Least-square support vector machine based cross-validations of the features extracted from the three nonlinear dynamics analysis methods achieve high classification rates, where those obtained from fuzzy recurrence plots are the highest.

关键词： Time series analysis Entropy Feature extraction Support vector machines nonlinear dynamical systems Parkinson's disease Biomedical measurement

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nonlinear dynamics of Contact Interaction of MEMS Beam Elements Accounting the Euler-Bernoulli Hypothesis in A Temperature Field 11

Nonlinear Dynamics of Contact Interaction of MEMS Beam Eleme...

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11th International IEEE Scientific and Technical conference on dynamics of Systems, Mechanisms and Machines (dynamics)

作者： Krysko, V. A. Saltykova, O. A. Krysko, A. V. Papkova, I. V. Yuri Gagarin State Tech Univ Saratov Russia

ISBN: (纸本)9781538618219;9781538618202

In this paper is proposed the methodology for determining the true chaos from the position of nonlinear dynamics for distributed mechanical systems in the form of a beam structure of two beams described by the kinematic first-approximation hypothesis (Euler-Bernoulli). There is a small gap between the beams. The lower beam (beam 2) will be considered as an elastic base for the upper beam (beam 1). The transverse distributed alternating load acts on beam 1. The contact interaction of the beams was taken into account by the Cantor model. This problem has a great nonlinearity due to the account of the geometric nonlinearity of beams according to T. von Karman and the constructive nonlinearity of the structure due to the contact interaction. Differential equations in partial derivatives reduce to the ODE system by the finite differences method (FDM) of the second order accuracy. The resulting system is solved by Runge-Kutta methods of various accuracy orders. In general case, the problem solution essentially depends on the methods of reducing partial differential equations to ODEs and methods for solving the Cauchy problem, boundary and initial conditions. When solving the problem by the method of finite differences with approximation O(h(2)), the solution will depend on the number of points of the integration interval partition and the time step in solving the Cauchy problem. The analysis of the obtained results is carried out by the nonlinear dynamics methods and the qualitative theory of differential equations. The results are compared for geometrically linear and nonlinear beams, taking into account the contact interaction. The mechanical structure is considered as a system with an infinite number of freedom degrees. A complete coincidence of solutions is achieved, depending on the partitions number in the spatial coordinate in the chaos. The sign of the first Lyapunov exponent is determined by the Kantz, Wolf and Rosenstein methods.

关键词： contact interaction first approximation beam model nonlinear dynamics finite differencies method geometric nonlinearity

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nonlinear dynamics of reactive EEG patterns under cerebrovascular and cardiovascular distortions 10

Nonlinear dynamics of reactive EEG patterns under cerebrovas...

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10th International conference on Chaotic Modeling and Simulation, chaos 2017

作者： Dick, Olga E. Pavlov Institute of Physiology of Russian Academy of Science St. Petersburg Russia

We examine the task of estimation of the differences in the human brain lability involving its opportunity to reproduce the external rhythm under cerebrovascular and cardiovascular distortions. For solving the task the electroencephalographic (EEG) patterns before, during and after intermittent photic stimulation are evaluated by the continuous wavelet transform and the recurrence quantification analysis. The degree of the human brain lability is estimated on the basis of changes in wavelet and recurrence features of the EEG patterns taking place under the photic stimulation. The coefficients of photic driving and holding and the energy increase times calculated by the wavelet spectra of the EEG patterns of patients with cerebrovascular and cardiovascular distortions differ significantly from the parameters determined for the healthy subjects. The study demonstrates the opportunity of nonlinear dynamics methods to estimate quantitatively the human brain lability of light stimulus perception for various groups of patients having cerebrovascular and cardiovascular distortions.

关键词： Wavelet transforms

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Visualization of amplitude-frequency characteristics of EEG of pathological and cognitive functions of the brain from a position of nonlinear dynamics

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Journal of Physics: conference Series 2019年第7期1260卷

作者： V A Krysko I V Papkova O A Saltykova T V Yakovleva S P Pavlov M V Zhigalov D Yu Petrov A V Krysko Department of Mathematics and Modelling Yuri Gagarin Saratov State Technical University Polytechnicheskaya st. 77 Saratov Russia 410054

In recent years, medical imaging methods have been intensively developed to provide comprehensive and extensive data for studying the work of the brain, which makes the present study relevant. The purpose of this work is to develop a new approach for analyzing EEG signals based on nonlinear dynamics methods. To achieve this goal, it is necessary to adapt the methods of nonlinear dynamics to solving EEG analysis tasks. In this paper, the following methods are used: the principal component method for noise clearance, the wavelet transform, the Wolf, Kanz, Rosenstein, neural networks methods to calculate the spectrum of the Lyapunov exponent (LCEs). Studies have shown that the chaos of the schizophrenic's EEG signals is higher than for healthy people. It has been revealed that the best visualization of the amplitude-frequency characteristics of the brain's EEG pathological functions is provided by the Morle and Gauss 32 wavelets.

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An advanced analysis and modelling the air pollutant concentration temporal dynamics in atmosphere of the industrial cities: Odessa city 1

An advanced analysis and modelling the air pollutant concent...

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1st International conference on Advances in Environmental Engineering (AEE)

作者： Buyadzhi, V. V. Glushkov, A. V. Khetselius, O. Yu Ternovsky, V. B. Serga, I. N. Bykowszczenko, N. Odessa State Environm Univ Lvovskaya Str 15 UA-65016 Odessa 16 Ukraine Tech Univ Szczecin Inst Chem & Environm Protect Piastow 42 Ave PL-71065 Szczecin Poland

Results of analysis and modelling the air pollutant (dioxide of nitrogen) concentration temporal dynamics in atmosphere of the industrial city Odessa are presented for the first time and based on computing by nonlinear methods of the chaos and dynamical systems theories. A chaotic behaviour is discovered and investigated. To reconstruct the corresponding strange chaotic attractor, the time delay and embedding dimension are computed. The former is determined by the methods of autocorrelation function and average mutual information, and the latter is calculated by means of correlation dimension method and algorithm of false nearest neighbours. It is shown that low-dimensional chaos exists in the nitrogen dioxide concentration time series under investigation. Further, the Lyapunov's exponents spectrum, Kaplan-Yorke dimension and Kolmogorov entropy are computed.

关键词： Dynamical systems

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nonlinear monetary policy rules in a pure exchange overlapping generations model

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JOURNAL OF EVOLUTIONARY ECONOMICS 2017年第5期27卷 1181-1203页

作者： Agliari, Anna Naimzada, Ahmad Pecora, Nicolo Catholic Univ Dept Econ & Social Sci Via Emilia Parmense 84 I-29100 Piacenza Italy Univ Milano Bicocca Dept Econ Quantitat Methods & Management Piazza Ateneo Nuovo 1 I-20126 Milan Italy

The dynamics of a pure exchange overlapping generations model with endogenous money growth rule is investigated. We consider a nonlinear monetary policy rule which, in each period, bounds the money growth rate so that money is determined by the deviation of the inflation rate from its target. More precisely, we introduce such a mechanism through a sigmoidal money adjustment mechanism characterized by the presence of two asymptotes that bound the money variation, and thus the dynamics. It is shown that, depending on the timing of the monetary policy and the degree of reaction of the Central Bank, the target equilibrium may be destabilized via different types of bifurcations. Multistability and coexistence of attractors may also occur and the study of the basins of attraction allows us to analyze the global dynamic properties of the economy under scrutiny. We find that active monetary policy rules may be relevant for their stabilizing properties, but they also may open the door to equilibrium cycles of any periodicity and even chaos.

关键词： OLG model nonlinear dynamics Monetary policy Stability Global bifurcations

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Chaotic dynamics size-dependent flexible rectangular flat shells

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Journal of Physics: conference Series 2019年第3期1158卷

作者： V A-ju Krysko I V Papkova V A Krysko 77 Politechnicheskaya street Saratov Russia 410054

In this paper was constructed mathematical model nonlinear vibrations flexible size-dependent spherical rectangular shell. Sheath viewed as a continuum Cosserat with constrained rotation of the particles (pseudo-continuum). The equations of motion of the shell element and the boundary conditions are obtained from the Ostrogradski-Hamilton energy principle on the basis of Kirchhoff-Love kinematic hypotheses. The geometric nonlinearity is taken into account by the model of T. von Karman. The equations of motion of the shell element in the work are written in a mixed form. A system of nonlinear partial differential equations reduces to an ODE system by the Bubnov-Galerkin method in higher approximations. The system is regarded as a system with an infinite number of degrees of freedom. The Cauchy problems are solved by methods of Runge-Kutta type from the second to the eighth order of accuracy. The convergence of each method depending on the time step and the number of terms in the expansion series of functions in the Bubnov-Galerkin method. The influence of the size-dependent parameter to the nonlinear dynamics of the rectangular plane into a spherical shell. The largest Lyapunov exponent is determined using three methods: Wolf, Kantz, and Rosenstein to prove the truth of chaos.

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Decomposing chaos into a harmonic oscillator with nonlinear feedback using pole placement methods 56

Decomposing chaos into a harmonic oscillator with nonlinear ...

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56th Annual IEEE conference on Decision and Control (CDC)

作者： Canyelles-Pericas, P. Dai, X. Binns, R. Busawon, K. Northumbria Univ Math Phys & Elect Engn Dept Newcastle Upon Tyne NE1 8ST Tyne & Wear England

ISBN: (纸本)9781509028733

This paper suggests a simple method for decomposing several chaotic systems into a harmonic oscillator provided with a nonlinear feedback. The chaotic oscillators analyzed include low order, non-delayed and continuous time models. The proposed decomposition method consists in three steps. First, the chaotic system is modelled as a combination of a linear component with a nonlinear feedback. Second, the linear part is modified so that it is transformed into a conventional harmonic oscillator with pole placement means. The position of the poles is set arbitrarily to guarantee its stability while maintaining the desired properties of sustained oscillation frequency. Finally, the feedback system is designed to keep the original nonlinearities while cancelling the changes introduced in the linear part. This, in turn, retrieves the initial chaotic dynamics. Essentially this procedure allows switching from chaotic to harmonic dynamics-or vice-versa- as required by application demands. The idea is presented in a generic form so that it can be applied to a variety of fields. The initial motivation was set in the context of secure chaotic communications. The decomposition procedure has been demonstrated and validated through numerical simulation of various well-known chaotic oscillators such as Duffing, Lorenz and Chua.

关键词： Artificial intelligence Three-dimensional displays 5G mobile communication conferences Australia FAA Iron

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Calculating Persistence Homology of Attractors in High-Dimensional Chaotic Systems

Calculating Persistence Homology of Attractors in High-Dimen...

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International conference on Computational Science and Computational Intelligence (CSCI)

作者： Xiong, Anda Assadi, Amir Cao, Yueqi Univ Wisconsin Dept Math Madison WI 53706 USA Beijing Inst Technol Dept Math Beijing Peoples R China

ISBN: (纸本)9781538626528

While persistent homology is a basic but useful tool for describing the topological features of spaces, it has rarely been applied to describe the chaotic attractor whose shape could be very intriguing and complex. Especially for high-dimensional chaotic attractors, on one hand it reveals the evolution and stability of dynamical systems yet on the other hand, since it is a natural restriction for human researchers that they are unable to see more than three dimensionalities, methods for categorizing high dimensional attractors are lacking. Therefore, in this article we propose the method of applying persistent homology calculation to high-dimensional chaotic attractors and give several representative examples from different genres of chaotic systems for whose topological structure being displayed.

关键词： nonlinear dynamics chaos Persistent Homology Strange Attractors Topology

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Study of Two-Memristor Circuit Model with Explicit Composition Method 24

Study of Two-Memristor Circuit Model with Explicit Compositi...

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24th IEEE International conference on Electronics, Circuits and Systems (ICECS)

作者： Butusov, Denis N. Ostrovskii, Valerii Y. Zubarev, Alexander V. St Petersburg Electrotech Univ LETI Dept Computer Aided Design St Petersburg Russia

ISBN: (纸本)9781538619117

This paper covers two important fields of research: composition ODE solvers and memristor-based circuit simulation. We considered a simple two-memristor chaotic circuit based on HP memristor model. A normalized ODE system is given as a mathematical model of the circuit. A finite-difference scheme obtained by new semi-explicit composition numerical method is represented. Phase space of the memristor circuit model and two high resolution dynamical maps are given as experimental findings. Backward error analysis for several numerical integration methods is described for the considered system.

关键词： dynamical chaos nonlinear dynamics memristor memristor-based circuits composition ODE solver numerical integration

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