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.

Pregnant crack addicts in a psychiatric unit

OBJECTIVE: In this study we aim to characterize a sample of 85 pregnant crack addicts admitted for detoxification in a psychiatric inpatient unit. METHOD: Cross-sectional study. Sociodemographic, clinical, obstetric and lifestyle information were evaluated. RESULTS: Age of onset for crack use varied from 11 to 35 years (median = 21). Approximately 25% of the patients smoked more than 20 crack rocks in a typical day of use (median = 10; min-max = 1-100). Tobacco (89.4%), alcohol (63.5%) and marijuana (51.8%) were the drugs other than crack most currently used. Robbery was reported by 32 patients (41.2%), imprisonment experience by 21 (24.7%), trade of sex for money/drugs by 38 (44.7%), home desertion by 33 (38.8%); 15.3% were positive for HIV, 5.9% for HCV, 1.2% for HBV and 8.2% for syphilis. After discharge from the psychiatric unit, only 25% of the sample followed the proposed treatment in the chemical dependency outpatient service. CONCLUSION: Greater risky behaviors for STD, as well as high rates of maternal HIV and Syphilis were found. Moreover, the high rates of concurrent use of other drugs and involvement in illegal activities contribute to show their chaotic lifestyles. Prevention and intervention programs need to be developed to address the multifactorial nature of this problem.

Spatial distribution of schistosomiasis foci on Itamaracá Island, Pernambuco, Brazil

Acute cases of schistosomiasis have been found on the coastal area of Pernambuco, Brazil, due to environmental disturbances and disorderly occupation of the urban areas. This study identifies and spatially marks the main foci of the snail host species, Biomphalaria glabrata on Itamaracá Island. The chaotic occupation of the beach resorts has favoured the emergence of transmission foci, thus exposing residents and tourists to the risk of infection. A database covering five years of epidemiological investigation on snails infected by Schistosoma mansoni in the island was produced with information from the geographic positioning of the foci, number of snails collected, number of snails tested positive, and their infection rate. The spatial position of the foci were recorded through the Global Positioning System (GPS), and the geographical coordinates were imported by AutoCad. The software packages ArcView and Spring were used for data processing and spatial analysis. AutoCad 2000 was used to plot the pairs of coordinates obtained from GPS. Between 1998 and 2002 5009 snails, of which 12.2% were positive for S. mansoni, were collected in Forte Beach. A total of 27 foci and areas of environmental risk were identified and spatially analyzed allowing the identification of the areas exposed to varying degrees of risk.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

Chaos in a Two-Degree of Freedom Duffing Oscillator

High dimensional dynamical systems has intricate behavior either on temporal or on spatial evolution properties. Nevertheless, most of the work on chaotic dynamics has been concentrated on temporal behavior of low-dimensional systems. This contribution is concerned with the chaotic response of a two-degree of freedom Duffing oscillator. Since the equations of motion are associated with a five-dimensional system, the analysis is performed by considering two Duffing oscillators, both with single-degree of freedom, coupled by a spring-dashpot system. With this assumption, it is possible to analyze the transmissibility of motion between the two oscillators.

Understanding the complexity in low dimensional systems

Complex System is any system that presents involved behavior, and is hard to be modeled by using the reductionist approach of successive subdivision, searching for ''elementary'' constituents. Nature provides us with plenty of examples of these systems, in fields as diverse as biology, chemistry, geology, physics, and fluid mechanics, and engineering. What happens, in general, is that for these systems we have a situation where a large number of both attracting and unstable chaotic sets coexist. As a result, we can have a rich and varied dynamical behavior, where many competing behaviors coexist. In this work, we present and discuss simple mechanical systems that are nice paradigms of Complex System, when they are subjected to random external noise. We argue that systems with few degrees of freedom can present the same complex behavior under quite general conditions.