Search results for: Poincare map

Authors: Mazhar B. Tayel, Eslam I. AlSaba

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The heart is the most important part in any body organisms. It effects and affected by any factor in the body. Therefore, it is a good detector of any matter in the body. When the heart signal is non-stationary signal, therefore, it should be study its variability. So, the Heart Rate Variability (HRV) has attracted considerable attention in psychology, medicine and have become important dependent measure in psychophysiology and behavioral medicine. Quantification and interpretation of heart rate variability. However, remain complex issues are fraught with pitfalls. This paper presents one of the non-linear techniques to analyze HRV. It discusses 'What Poincare plot is?', 'How it is work?', 'its usage benefits especially in HRV', 'the limitation of Poincare cause of standard deviation SD1, SD2', and 'How overcome this limitation by using complex correlation measure (CCM)'. The CCM is most sensitive to changes in temporal structure of the Poincaré plot as compared to SD1 and SD2.

Keywords: heart rate variability, chaotic system, poincare, variance, standard deviation, complex correlation measure

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Authors: Ali Albadri

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Step band in an escalator moves in a cyclic periodic pattern. Similarly, most if not all of the components and sub-assemblies in the escalator operate in the same way. If you mark up one step in the step band of an escalator and stand next to the escalator, on the incline, to watch the marked-up step when it passes by, you ask yourself, does the marked up step behaves exactly the same way during each revolution when it passes you by again and again? We can say that; there is some similarity in this example and the example when an astronomer watches planets in the sky, and he or she asks himself or herself, does each planet intersects the plan of observation in the same position for every pantry rotation? For a fact, we know for the answer to the second example is no, because scientist, astronomers, and mathematicians have proven that planets deviate from their paths to take new paths during their planetary moves, albeit with minimal change. But what about the answer to the question in the first example? considering that there is increase in the wear and tear of components with time in the step, in the step band, in the tracks and in many other places in the escalator. There is also the accumulation of fatigue in the components and sub-assemblies. This research is part of many studies which we are conducting to address the answer for the question in the first example. We have been using the fractal dimension as a quantities tool and the Poincare map as a qualitative tool. This study has shown that the fractal dimension value and the shape and distribution of the orbits in the Poincare map has significant correlation with the quality of the mechanical components and sub-assemblies in the escalator.

Keywords: fractal dimension, Poincare map, rugby ball orbit, worm orbit

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Authors: Mitsuyoshi Tomiya, Kentaro Kawamura, Shoichi Sakamoto

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In chaotic billiard systems, scar-like localization has been found on time-evolving wave packet. We may call it the “dynamical scar” to separate it to the original scar in stationary states. It also comes out along the vicinity of classical unstable periodic orbits, when the wave packets are launched along the orbits, against the hypothesis that the waves become homogenous all around the billiard. Then time-evolving wave packets are investigated numerically in phase space. The Wigner function is adopted to detect the wave packets in phase space. The 2-dimensional Poincaré sections of the 4-dimensional phase space are introduced to clarify the dynamical behavior of the wave packets. The Poincaré sections of the coordinate (x or y) and the momentum (Px or Py) can visualize the dynamical behavior of the wave packets, including the behavior in the momentum degree also. For example, in “dynamical scar” states, a bit larger momentum component comes first, and then the a bit smaller and smaller components follow next. The sections made in the momentum space (Px or Py) elucidates specific trajectories that have larger contribution to the “dynamical scar” states. It is the fixed point observation of the momentum degrees at a specific fixed point(x0, y0) in the phase space. The accumulation are also calculated to search the “dynamical scar” in the Poincare sections. It is found the scars as bright spots in momentum degrees of the phase space.

Keywords: chaotic billiard, Poincaré section, scar, wave packet

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Authors: Adedayo Oke Adelakun

Abstract:

The chaotic dynamics of periodically forced oscillators with smooth potential has been extensively investigated via theoretical, numerical and experimental simulations. With the advent of the study of chaotic dynamics by means of method of multiple time scale analysis, Melnikov theory, bifurcation diagram, Poincare's map, bifurcation diagrams and Lyapunov exponents, it has become necessary to seek for a better understanding of nonlinear oscillator with noisy term. In this paper, we examine the influence of noise on complex dynamical behaviour of periodically forced F6 - Duffing oscillator for specific choice of noisy parameters. The inclusion of noisy term improves the dynamical behaviour of the oscillator which may have wider application in secure communication than smooth potential.

Keywords: hierarchical structure, periodically forced oscillator, noisy parameters, dynamical behaviour, F6 - duffing oscillator

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Authors: Akshay B. Pawar, Rohit Y. Parasnis

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Heart Rate Variability (HRV) is a widely used indicator of the regulation between the autonomic nervous system (ANS) and the cardiovascular system. Besides being non-invasive, it also has the potential to predict mortality in cases involving critical injuries. The gold standard method for determining HRV is based on the analysis of RR interval time series extracted from ECG signals. However, because it is much more convenient to obtain photoplethysmogramic (PPG) signals as compared to ECG signals (which require the attachment of several electrodes to the body), many researchers have used pulse cycle intervals instead of RR intervals to estimate HRV. They have also compared this method with the gold standard technique. Though most of their observations indicate a strong correlation between the two methods, recent studies show that in healthy subjects, except for a few parameters, the pulse-based method cannot be a surrogate for the standard RR interval- based method. Moreover, the former tends to overestimate short-term variability in heart rate. This calls for improvements in or alternatives to the pulse-cycle interval method. In this study, besides the systolic peak-peak interval method (PP method) that has been studied several times, four recent PPG-based techniques, namely the first derivative peak-peak interval method (P1D method), the second derivative peak-peak interval method (P2D method), the valley-valley interval method (VV method) and the tangent-intersection interval method (TI method) were compared with the gold standard technique. ECG and PPG signals were obtained from 10 young and healthy adults (consisting of both males and females) seated in the armchair position. In order to de-noise these signals and eliminate baseline drift, they were passed through certain digital filters. After filtering, the following HRV parameters were computed from PPG using each of the five methods and also from ECG using the gold standard method: time domain parameters (SDNN, pNN50 and RMSSD), frequency domain parameters (Very low-frequency power (VLF), Low-frequency power (LF), High-frequency power (HF) and Total power or “TP”). Besides, Poincaré plots were also plotted and their SD1/SD2 ratios determined. The resulting sets of parameters were compared with those yielded by the standard method using measures of statistical correlation (correlation coefficient) as well as statistical agreement (Bland-Altman plots). From the viewpoint of correlation, our results show that the best PPG-based methods for the determination of most parameters and Poincaré plots are the P2D method (shows more than 93% correlation with the standard method) and the PP method (mean correlation: 88%) whereas the TI, VV and P1D methods perform poorly (<70% correlation in most cases). However, our evaluation of statistical agreement using Bland-Altman plots shows that none of the five techniques agrees satisfactorily well with the gold standard method as far as time-domain parameters are concerned. In conclusion, excellent statistical correlation implies that certain PPG-based methods provide a good amount of information on the pattern of heart rate variation, whereas poor statistical agreement implies that PPG cannot completely replace ECG in the determination of HRV.

Keywords: photoplethysmography, heart rate variability, correlation coefficient, Bland-Altman plot

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Authors: Paolo Russu

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The purpose of the present paper is to highlight some features of an economic growth model with environmental negative externalities, giving rise to a three-dimensional dynamic system. In particular, we show that the economy, which is based on a Perfect-Substitution Technologies function of production, has no neither indeterminacy nor poverty trap. This implies that equilibrium select by economy depends on the history (initial values of state variable) of the economy rather than on expectations of economies agents. Moreover, by contrast, we prove that the basin of attraction of locally equilibrium points may be very large, as they can extend up to the boundary of the system phase space. The infinite-horizon optimal control problem has the purpose of maximizing the representative agent’s instantaneous utility function depending on leisure and consumption.

Keywords: Hopf bifurcation, open-access natural resources, optimal control, perfect-substitution technologies, Poincarè compactification

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Authors: Kais Siala, Mohamed Kharrat, Mohamed Abid

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Exposure therapies encourage patients to gradually begin facing their painful memories of the trauma in order to reduce fear and anxiety. In this context, virtual reality techniques are widely used for treatment of different kinds of phobia. The particular case of fear of death phobia (thanataphobia) is addressed in this paper. For this purpose, we propose to make a simulation of Near Death Experience (NDE) using augmented reality techniques. We propose in particular to simulate the Out-of-Body experience (OBE) which is the first step of a Near-Death-Experience (NDE). In this paper, we present technical aspects of this simulation as well as short-term impact in terms of physiological measures. The non-linear Poincéré plot is used to describe the difference in Heart Rate Variability between In-Body and Out-Of-Body conditions.

Keywords: Out-of-Body simulation, physiological measure, augmented reality, phobia psychotherapy, HRV, Poincaré plot

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Authors: S. Kida

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We consider the flow of an incompressible viscous fluid in a precessing sphere whose spin and precession axes are orthogonal to each other. The flow is characterized by two non-dimensional parameters, the Reynolds number Re and the Poincare number Po. For which values of (Re, Po) will the flow approach a steady state from an arbitrary initial condition? To answer it we are searching the instability boundary of the steady states in the whole (Re, Po) plane. Here, we focus the rapidly rotating and weakly precessing limit, i.e., Re >> 1 and Po << 1. The steady flow was obtained by the asymptotic expansion for small ε=Po Re¹/² << 1. The flow exhibits nearly a solid-body rotation in the whole sphere except for a thin boundary layer which develops over the sphere surface. The thickness of this boundary layer is of O(δ), where δ=Re⁻¹/², except where two circular critical bands of thickness of O(δ⁴/⁵) and of width of O(δ²/⁵) which are located away from the spin axis by about 60°. We perform the linear stability analysis of the steady flow. We assume that the disturbances are localized in the critical bands and make an expansion analysis in terms of ε to derive the eigenvalue problem for the growth rate of the disturbance, which is solved numerically. As the solution, we obtain an asymptote of the stability boundary as Po=28.36Re⁻⁰.⁸. This agrees excellently with the corresponding laboratory experiments and numerical simulations. One of the most popular instability mechanisms so far is the parametric instability, which turns out, however, not to give the correct stability boundary. The present instability is different from the parametric instability.

Keywords: boundary layer, critical band, instability, precessing sphere

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Authors: Morteza Shayan Arani, Mohammadamin Esmailzadehazimi, Mohammadreza Moeini, Mohammad Toorani, Aouni A. Lakis

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This paper investigates the nonlinear response of thin, incompressible, hyperelastic cylindrical shells in the presence of a time-varying temperature field while considering initial geometric imperfections. The governing equations of motion are derived using an improved Donnell's shallow shell theory. The hyperelastic material is modeled using the Mooney-Rivlin model with two parameters, incorporating temperature-dependent terms. The Lagrangian method is applied to obtain the equation of motion. The resulting governing equation is addressed through the Lindstedt-Poincaré and Multiple Scale methods. The linear and nonlinear models presented in this study are verified against existing open literature, demonstrating the accuracy and reliability of the presented model. The study focuses on understanding the influence of temperature variations and geometrical imperfections on the natural frequency and amplitude-frequency response of the systems. Notably, the investigation reveals the coexistence of hardening and softening peaks in the amplitude-frequency response, which vary in magnitude depending on these parameters. Additionally, resonance peaks exhibit changes as a result of temperature and geometric imperfections.

Keywords: hyperelastic material, cylindrical shell, geometrical nonlinearity, material naolinearity, initial geometric imperfection, temperature gradient, hardening and softening

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Authors: Kwan U. Kim, Jin Sim, Ryong Jin Jang, Sung Duk Kim

Abstract:

108 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not correctly solve one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition to it, they did not treat the astronomical and physical phenomena in a physical way based on the correct physical laws obtained from the solution of the geodesic equations in Schwarzschild metric. Therefore, some former scholars mentioned that Einstein’s theoretical basis of the general theory of relativity was obscure and incorrect, but they have not given a correct physical solution to the problems. Furthermore, since the general theory of relativity has not given a quantitative solution to obscure and incorrect problems, the generalization of gravitational theory has not been successfully completed yet, although the former scholars thought of it and tried to do it. In order to solve the problems it is necessary to explore the obscure and incorrect problems in general theory of relativity based on the physical laws and to find out the methodology of solving the problems. Therefore, first of all, as the first step for achieving the purpose, the right solution of the geodesic equation in Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results have been presented, the obscure and incorrect problems have been shown, and an analysis of them has been made based on the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild, Poincaré

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Authors: Kwan U. Kim, Jin Sim, Ryong Jin Jang, Sung Duk Kim

Abstract:

108 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in the Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not correctly solve one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition, they did not treat the astronomical and physical phenomena in a physical way based on the correct physical laws obtained from the solution of the geodesic equations in the Schwarzschild metric. Therefore, some former scholars mentioned that Einstein’s theoretical basis of a general theory of relativity was obscure and incorrect, but they did not give a correct physical solution to the problems. Furthermore, since the general theory of relativity has not given a quantitative solution to obscure and incorrect problems, the generalization of gravitational theory has not yet been successfully completed, although former scholars have thought of it and tried to do it. In order to solve the problems, it is necessary to explore the obscure and incorrect problems in a general theory of relativity based on the physical laws and to find out the methodology for solving the problems. Therefore, as the first step toward achieving this purpose, the right solution of the geodesic equation in the Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results have been presented, the obscure and incorrect problems have been shown, and an analysis of them has been made based on the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild, Poincaré

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Authors: Reeta Devi, Hitender Kumar Tyagi, Dinesh Kumar

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In present scenario, cardiovascular problems are growing challenge for researchers and physiologists. As heart disease have no geographic, gender or socioeconomic specific reasons; detecting cardiac irregularities at early stage followed by quick and correct treatment is very important. Electrocardiogram is the finest tool for continuous monitoring of heart activity. Heart rate variability (HRV) is used to measure naturally occurring oscillations between consecutive cardiac cycles. Analysis of this variability is carried out using time domain, frequency domain and non-linear parameters. This paper presents HRV analysis of the online dataset for normal sinus rhythm (taken as healthy subject) and sudden cardiac death (SCD subject) using all three methods computing values for parameters like standard deviation of node to node intervals (SDNN), square root of mean of the sequences of difference between adjacent RR intervals (RMSSD), mean of R to R intervals (mean RR) in time domain, very low-frequency (VLF), low-frequency (LF), high frequency (HF) and ratio of low to high frequency (LF/HF ratio) in frequency domain and Poincare plot for non linear analysis. To differentiate HRV of healthy subject from subject died with SCD, k –nearest neighbor (k-NN) classifier has been used because of its high accuracy. Results show highly reduced values for all stated parameters for SCD subjects as compared to healthy ones. As the dataset used for SCD patients is recording of their ECG signal one hour prior to their death, it is therefore, verified with an accuracy of 95% that proposed algorithm can identify mortality risk of a patient one hour before its death. The identification of a patient’s mortality risk at such an early stage may prevent him/her meeting sudden death if in-time and right treatment is given by the doctor.

Keywords: early stage prediction, heart rate variability, linear and non-linear analysis, sudden cardiac death

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Authors: Jin Liang, James H. Liu, Ti-Jun Xiao

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It is known that there exist many physical phenomena where abrupt or impulsive changes occur either in the system dynamics, for example, ad-hoc network, or in the input forces containing impacts, for example, the bombardment of space antenna by micrometeorites. There are many other examples such as ultra high-speed optical signals over communication networks, the collision of particles, inventory control, government decisions, interest changes, changes in stock price, etc. These are impulsive phenomena. Hence, as a combination of the traditional initial value problems and the short-term perturbations whose duration can be negligible in comparison with the duration of the process, the systems with impulsive conditions (i.e., impulsive systems) are more realistic models for describing the impulsive phenomenon. Such a situation is also suitable for the delay systems, which include some of the past states of the system. So far, there have been a lot of research results in the study of impulsive systems with delay both in finite and infinite dimensional spaces. In this paper, we investigate the periodicity of solutions to the nonautonomous impulsive evolution equations with infinite delay in Banach spaces, where the coefficient operators (possibly unbounded) in the linear part depend on the time, which are impulsive systems in infinite dimensional spaces and come from the optimal control theory. It was indicated that the study of periodic solutions for these impulsive evolution equations with infinite delay was challenging because the fixed point theorems requiring some compactness conditions are not applicable to them due to the impulsive condition and the infinite delay. We are happy to report that after detailed analysis, we are able to combine the techniques developed in our previous papers, and some new ideas in this paper, to attack these impulsive evolution equations and derive periodic solutions. More specifically, by virtue of the related transition operator family (evolution family), we present a Poincaré operator given by the nonautonomous impulsive evolution system with infinite delay, and then show that the operator is a condensing operator with respect to Kuratowski's measure of non-compactness in a phase space by using an Amann's lemma. Finally, we derive periodic solutions from bounded solutions in view of the Sadovskii fixed point theorem. We also present a relationship between the boundedness and the periodicity of the solutions of the nonautonomous impulsive evolution system. The new results obtained here extend some earlier results in this area for evolution equations without impulsive conditions or without infinite delay.

Keywords: impulsive, nonautonomous evolution equation, optimal control, periodic solution

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