Route to chaos in a third-order phase-locked loop network

Phase-locked loops (PLLs) are widely used in applications related to control systems and telecommunication networks. Here we show that a single-chain master-slave network of third-order PLLs can exhibit stationary, periodic and chaotic behaviors, when the value of a single parameter is varied. Hopf, period-doubling and saddle-saddle bifurcations are found. Chaos appears in dissipative and non-dissipative conditions. Thus, chaotic behaviors with distinct dynamical features can be generated. A way of encoding binary messages using such a chaos-based communication system is suggested. (C) 2009 Elsevier B.V. All rights reserved.

Statements on chaos control designs, including a fractional order dynamical system, applied to a MEMS comb-drive actuator

In this work, we deal with a micro electromechanical system (MEMS), represented by a micro-accelerometer. Through numerical simulations, it was found that for certain parameters, the system has a chaotic behavior. The chaotic behaviors in a fractional order are also studied numerically, by historical time and phase portraits, and the results are validated by the existence of positive maximal Lyapunov exponent. Three control strategies are used for controlling the trajectory of the system: State Dependent Riccati Equation (SDRE) Control, Optimal Linear Feedback Control, and Fuzzy Sliding Mode Control. The controls proved effective in controlling the trajectory of the system studied and robust in the presence of parametric errors.

On a control design to an AFM microcantilever beam, operating in a tapping-mode, with irregular behavior

In last decades, control of nonlinear dynamic systems became an important and interesting problem studied by many authors, what results the appearance of lots of works about this subject in the scientific literature. In this paper, an Atomic Force Microscope micro cantilever operating in tapping mode was modeled, and its behavior was studied using bifurcation diagrams, phase portraits, time history, Poincare maps and Lyapunov exponents. Chaos was detected in an interval of time; those phenomena undermine the achievement of accurate images by the sample surface. In the mathematical model, periodic and chaotic motion was obtained by changing parameters. To control the chaotic behavior of the system were implemented two control techniques. The SDRE control (State Dependent Riccati Equation) and Time-delayed feedback control. Simulation results show the feasibility of the bothmethods, for chaos control of an AFM system. Copyright © 2011 by ASME.

O uso da análise de Fourier, de Wavelets e dos expoentes de Lyapunov no estudo de um sistema dinâmico não-ideal com atrito seco e excitação externa

Pós-graduação em Física - IGCE

Dinâmica não linear, caos, e controle na microscopia de força atômica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dinâmica não linear e controle de um sistema vibratório modelado com memória de forma e, excitado por fontes de energia do tipo ideal e não ideal

Pós-graduação em Engenharia Mecânica - FEB

Hero's journey in bifurcation diagram

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films. (C) 2011 Elsevier B.V. All rights reserved.

Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving

Chaotic systems, when used to drive copies of themselves (or parts of themselves) may induce interesting behaviors in the driven system. In case the later exhibits invariance under amplification or translation, they may show amplification (reduction), or displacement of the attractor. It is shown how the behavior to be obtained is implied by the symmetries involved. Two explicit examples are studied to show how these phenomena manifest themselves under perfect and imperfect coupling.

Chaotic systems with a null conditional Lyapunov exponent under nonlinear driving.

Control of a chaotic system by homogeneous nonlinear driving, when a conditional Lyapunov exponent is zero, may give rise to special and interesting synchronizationlike behaviors in which the response evolves in perfect correlation with the drive. Among them, there are the amplification of the drive attractor and the shift of it to a different region of phase space. In this paper, these synchronizationlike behaviors are discussed, and demonstrated by computer simulation of the Lorentz model [E. N. Lorenz, J. Atmos. Sci. 20 130 (1963)] and the double scroll [T. Matsumoto, L. O. Chua, and M. Komuro, IEEE Trans. CAS CAS-32, 798 (1985)].

Nonlinear control in an electromechanical transducer with chaotic behaviour

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Behaviors and hygiene habits of complete denture wearers

In this study, a questionnaire was applied to patients from Ribeirão Preto Dental School, University of São Paulo, Brazil, to evaluate the hygiene methods and habits concerning the use of complete dentures, the age of dentures, and whether patients have been instructed on how to clean their dentures. The mean age of patients was 63.35 years, and most of them were females (82.08%). The results showed that 62.26% of the respondents had been using the same maxillary complete denture for more than 5 years, and 49.06% used the same mandible complete denture for more than 5 years. Of the patients interviewed, 58.49% slept with the dentures. Mechanical brushing was the most used cleaning method by the patients (100%), using water, dentifrice and toothbrush (84.91%). Most patients (51.89%) reported never having been instructed by their dentists as to how to clean their dentures. Based on the limitations of this study, it was concluded that the patients interviewed had limited knowledge about prosthetic hygiene and oral care. The method more used by patients was the mechanical method of brushing, most patients used the same complete dentures for more than 5 years and slept with the dentures.

Long-term social recognition memory in adult male rats: factor analysis of the social and non-social behaviors

A modified version of the intruder-resident paradigm was used to investigate if social recognition memory lasts at least 24 h. One hundred and forty-six adult male Wistar rats were used. Independent groups of rats were exposed to an intruder for 0.083, 0.5, 2, 24, or 168 h and tested 24 h after the first encounter with the familiar or a different conspecific. Factor analysis was employed to identify associations between behaviors and treatments. Resident rats exhibited a 24-h social recognition memory, as indicated by a 3- to 5-fold decrease in social behaviors in the second encounter with the same conspecific compared to those observed for a different conspecific, when the duration of the first encounter was 2 h or longer. It was possible to distinguish between two different categories of social behaviors and their expression depended on the duration of the first encounter. Sniffing the anogenital area (49.9% of the social behaviors), sniffing the body (17.9%), sniffing the head (3%), and following the conspecific (3.1%), exhibited mostly by resident rats, characterized social investigation and revealed long-term social recognition memory. However, dominance (23.8%) and mild aggression (2.3%), exhibited by both resident and intruders, characterized social agonistic behaviors and were not affected by memory. Differently, sniffing the environment (76.8% of the non-social behaviors) and rearing (14.3%), both exhibited mostly by adult intruder rats, characterized non-social behaviors. Together, these results show that social recognition memory in rats may last at least 24 h after a 2-h or longer exposure to the conspecific.

Morphine infusions into the rostrolateral periaqueductal gray affect maternal behaviors

It is well established that morphine inhibits maternal behaviors. Previous studies by our group have shown activation of the rostrolateral periaqueductal gray (rlPAG) upon inhibition-intended subcutaneous injections of morphine. In this context, we demonstrated that a single naloxone infusion into the rlPAG, following this opioid-induced inhibition, reactivated maternal behaviors. Since these data were obtained by using peripheral morphine injections, the present study was designed to test whether morphine injected directly into the rlPAG would affect maternal behaviors. Our hypothesis that morphine acting through the rlPAG would disrupt maternal behaviors was confirmed with a local infusion of morphine. The mothers showed shorter latency for locomotor behavior to explore the home cage (P = 0.049). Inhibition was especially evident regarding retrieving (P = 0.002), nest building (P = 0.05) and full maternal behavior (P = 0.023). These results support the view that opioidergic transmission plays a behaviorally meaningful inhibitory role in the rostrolateral PAG.

Interactive Brazilian program to prevent eating disorders behaviors: a pilot study

During a four month scholarly leave in United States of America, researchers designed a culturally appropriate prevention program for eating disorders (ED) for Brazilian adolescent girls. The program "Se Liga na Nutrição" was modeled on other effective programs identified in a research literature review and was carried out over eleven interactive sessions. It was positively received by the adolescents who suggested that it be part of school curricula. The girls reported that it helped them to develop critical thinking skills with regards to sociocultural norms about body image, food and eating practices

Chaotic Patterns in Aeroelastic Signals

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincare sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincare mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents. Copyright (C) 2009 F. D. Marques and R. M. G. Vasconcellos.