Estimating Attractor Dimension on the Nonlinear Pendulum Time Series

Chaotic dynamical systems exhibit trajectories in their phase space that converges to a strange attractor. The strangeness of the chaotic attractor is associated with its dimension in which instance it is described by a noninteger dimension. This contribution presents an overview of the main definitions of dimension discussing their evaluation from time series employing the correlation and the generalized dimension. The investigation is applied to the nonlinear pendulum where signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the time series. State space reconstruction and the determination of attractor dimensions are carried out regarding periodic and chaotic signals. Results obtained from time series analyses are compared with a reference value obtained from the analysis of mathematical model, estimating noise sensitivity. This procedure allows one to identify the best techniques to be applied in the analysis of experimental data.

Simulation of Steady-State Nonlinear Heat Transfer Problems Through the Minimization of Quadratic Functionals

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.

Experimental Vibration Characteristics of a Beam with Nonlinear Support Using Receptance Coupling Analysis

This paper applies the Multi-Harmonic Nonlinear Receptance Coupling Approach (MUHANORCA) (Ferreira 1998) to evaluate the frequency response characteristics of a beam which is clamped at one end and supported at the other end by a nonlinear cubic stiffness joint. In order to apply the substructure coupling technique, the problem was characterised by coupling a clamped linear beam with a nonlinear cubic stiffness joint. The experimental results were obtained by a sinusoidal excitation with a special force control algorithm where the level of the fundamental force is kept constant and the level of the harmonics is kept zero for all the frequencies measured.

Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study

In this paper is Analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. The dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. In this critical point, a Hopf bifurcation occurs. In this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). This local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.

Sawtooth waves during REM sleep after administration of haloperidol combined with total sleep deprivation in healthy young subjects

We sought to examine the possible participation of dopaminergic receptors in the phasic events that occur during rapid eye movement (REM) sleep, known as sawtooth waves (STW). These phasic phenomena of REM sleep exhibit a unique morphology and, although they represent a characteristic feature of REM sleep, little is known about the mechanisms which generate them and which are apparently different from rapid eye movements. STW behavior was studied in 10 male volunteers aged 20 to 35 years, who were submitted to polysomnographic monitoring (PSG). On the adaptation night they were submitted to the first PSG and on the second night, to the basal PSG. On the third night the volunteers received placebo or haloperidol and spent the whole night awake. On the fourth night they were submitted to the third PSG. After a 15-day rest period, the volunteers returned to the sleep laboratory and, according to a double-blind crossover randomized design, received haloperidol or placebo and spent the whole night awake, after which they were submitted to the fourth PSG. The volunteers who were given haloperidol combined with sleep deprivation exhibited an elevation of the duration and density of the STW, without significant alterations of the other REM sleep phasic phenomena such as rapid eye movement. These findings suggest that sawtooth waves must have their own generating mechanisms and that the dopaminergic receptors must exert a modulating role since REM sleep deprivation, as well as administration of neuroleptics, produces supersensitivity of dopaminergic receptors.

Linear and nonlinear analysis of heart rate variability in healthy subjects and after acute myocardial infarction in patients

The objectives of this study were to evaluate and compare the use of linear and nonlinear methods for analysis of heart rate variability (HRV) in healthy subjects and in patients after acute myocardial infarction (AMI). Heart rate (HR) was recorded for 15 min in the supine position in 10 patients with AMI taking β-blockers (aged 57 ± 9 years) and in 11 healthy subjects (aged 53 ± 4 years). HRV was analyzed in the time domain (RMSSD and RMSM), the frequency domain using low- and high-frequency bands in normalized units (nu; LFnu and HFnu) and the LF/HF ratio and approximate entropy (ApEn) were determined. There was a correlation (P < 0.05) of RMSSD, RMSM, LFnu, HFnu, and the LF/HF ratio index with the ApEn of the AMI group on the 2nd (r = 0.87, 0.65, 0.72, 0.72, and 0.64) and 7th day (r = 0.88, 0.70, 0.69, 0.69, and 0.87) and of the healthy group (r = 0.63, 0.71, 0.63, 0.63, and 0.74), respectively. The median HRV indexes of the AMI group on the 2nd and 7th day differed from the healthy group (P < 0.05): RMSSD = 10.37, 19.95, 24.81; RMSM = 23.47, 31.96, 43.79; LFnu = 0.79, 0.79, 0.62; HFnu = 0.20, 0.20, 0.37; LF/HF ratio = 3.87, 3.94, 1.65; ApEn = 1.01, 1.24, 1.31, respectively. There was agreement between the methods, suggesting that these have the same power to evaluate autonomic modulation of HR in both AMI patients and healthy subjects. AMI contributed to a reduction in cardiac signal irregularity, higher sympathetic modulation and lower vagal modulation.

Long-term correlation of the electrocorticogram as a bioindicator of brain exposure to ionizing radiation

Understanding the effects of radiation and its possible influence on the nervous system are of great clinical interest. However, there have been few electrophysiological studies on brain activity after exposure to ionizing radiation (IR). A new methodological approach regarding the assessment of the possible effects of IR on brain activity is the use of linear and nonlinear mathematical methods in the analysis of complex time series, such as brain oscillations measured using the electrocorticogram (ECoG). The objective of this study was to use linear and nonlinear mathematical methods as biomarkers of gamma radiation regarding cortical electrical activity. Adult Wistar rats were divided into 3 groups: 1 control and 2 irradiated groups, evaluated at 24 h (IR24) and 90 days (IR90) after exposure to 18 Gy of gamma radiation from a cobalt-60 radiotherapy source. The ECoG was analyzed using power spectrum methods for the calculation of the power of delta, theta, alpha and beta rhythms and by means of the α-exponent of the detrended fluctuation analysis (DFA). Using both mathematical methods it was possible to identify changes in the ECoG, and to identify significant changes in the pattern of the recording at 24 h after irradiation. Some of these changes were persistent at 90 days after exposure to IR. In particular, the theta wave using the two methods showed higher sensitivity than other waves, suggesting that it is a possible biomarker of exposure to IR.