ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

Análise das forças de reação vertical do solo em função das variações dos centros de massa de indivíduos a partir de movimentos de tronco com variação de carga

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo da estabilidade a pequenas perturbações do sistema elétrico de potência sob a ação do dispositivo FACTS PHASE SHIFTER - PS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A dinâmica dos sistemas de produção praticados em uma unidade de conservação de uso direto na Amazônia - a Reserva Extrativista do Rio Cajari no estado do Amapá.

Este trabalho aborda um tipo específico de extrativismo: o extrativismo da castanha-do-brasil realizado na Reserva Extrativista do rio Cajari no Estado do Amapá (RESEX/CA). O trabalho é uma continuidade de pesquisas realizadas no ano de 2000, e tem como foco principal compreender a dinâmica dos sistemas de produção praticados na RESEX/CA. Neste trabalho percebemos que as mudanças ocorridas nos sistemas de produção praticados na RESEX/CA de 2000 para 2005, evidenciam que além de fatores de ordem econômica, a permanência das práticas agrícolas com o extrativismo da castanha se rege por outros fatores. A relação histórica de uso da floresta com o extrativismo e as agriculturas é bem mais complexa, não podendo ser avaliada apenas do prisma econômico. Os dados demonstram que as unidades de produção extrativistas são aquelas de menor desempenho econômico, e, apesar disso, não há um movimento das famílias em acabar com esse sistema. Ao contrário, o tipo extrativista não apenas se manteve, mas aumentou de representatividade de 2000 para 2005, indicando atratividade deste tipo para as famílias da RESEX/CA. Entretanto, os sistemas agroextrativistas também cresceram, indicando que algumas famílias procuram alcançar melhores níveis de qualidade de vida, através da agricultura. Em se tratando de uma unidade de conservação de uso direto, para esta reserva extrativista deveria ser direcionada ações de apoio aos castanheiros da RESEX/CA, para que eles pudessem ter melhores condições de vida, sem ter que investir em outras atividades, que não o extrativismo.

Description of the attainable sets of one-dimensional differential inclusions

The role played by the attainable set of a differential inclusion, in the study of dynamic control systems and fuzzy differential equations, is widely acknowledged. A procedure for estimating the attainable set is rather complicated compared to the numerical methods for differential equations. This article addresses an alternative approach, based on an optimal control tool, to obtain a description of the attainable sets of differential inclusions. In particular, we obtain an exact delineation of the attainable set for a large class of nonlinear differential inclusions.

Aplicações médicas das abordagens complexas não lineares: a geometria fractal do EEG

Pós-graduação em Saúde Coletiva - FMB

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Detection of gait perturbations based on proprioceptive information. Application to Limit Cycle Walkers

Walking on irregular surfaces and in the presence of unexpected events is a challenging problem for bipedal machines. Up to date, their ability to cope with gait disturbances is far less successful than humans': Neither trajectory controlled robots, nor dynamic walking machines (Limit CycleWalkers) are able to handle them satisfactorily. On the contrary, humans reject gait perturbations naturally and efficiently relying on their sensory organs that, if needed, elicit a recovery action. A similar approach may be envisioned for bipedal robots and exoskeletons: An algorithm continuously observes the state of the walker and, if an unexpected event happens, triggers an adequate reaction. This paper presents a monitoring algorithm that provides immediate detection of any type of perturbation based solely on a phase representation of the normal walking of the robot. The proposed method was evaluated in a Limit Cycle Walker prototype that suffered push and trip perturbations at different moments of the gait cycle, providing 100% successful detections for the current experimental apparatus and adequately tuned parameters, with no false positives when the robot is walking unperturbed.

Dynamische Standsicherheit von Portalstaplern

Der Artikel beschreibt die Untersuchung der dynamischen Standsicherheit von Portalstaplern. Dazu wurde ein aktueller repräsentativer Portalstapler analysiert und in ein Mehrkörper-Simulationsmodell abgebildet. Die Validierung des Modells erfolgte auf Basis von Messfahrten am realen System. Aus den durchgeführten Simulationsstudien wurden technische Verbesserungsmaßnahmen abgeleitet, welche die dynamische Standsicherheit von Portalstaplern erhöhen.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Application of a computational model for complex fluvial ecosystems: The population dynamics of zebra mussel Dreissena polymorpha as a case study

The potential and adaptive flexibility of population dynamic P-systems (PDP) to study population dynamics suggests that they may be suitable for modelling complex fluvial ecosystems, characterized by a composition of dynamic habitats with many variables that interact simultaneously. Using as a model a reservoir occupied by the zebra mussel Dreissena polymorpha, we designed a computational model based on P systems to study the population dynamics of larvae, in order to evaluate management actions to control or eradicate this invasive species. The population dynamics of this species was simulated under different scenarios ranging from the absence of water flow change to a weekly variation with different flow rates, to the actual hydrodynamic situation of an intermediate flow rate. Our results show that PDP models can be very useful tools to model complex, partially desynchronized, processes that work in parallel. This allows the study of complex hydroecological processes such as the one presented, where reproductive cycles, temperature and water dynamics are involved in the desynchronization of the population dynamics both, within areas and among them. The results obtained may be useful in the management of other reservoirs with similar hydrodynamic situations in which the presence of this invasive species has been documented.

In vivo compatibility of Dynesys(®) spinal implants: a case series of five retrieved periprosthetic tissue samples and corresponding implants

PURPOSE To determine whether particulate debris is present in periprosthetic tissue from revised Dynesys(®) devices, and if present, elicits a biological tissue reaction. METHODS Five Dynesys(®) dynamic stabilization systems consisting of pedicle screws (Ti alloy), polycarbonate-urethane (PCU) spacers and a polyethylene-terephthalate (PET) cord were explanted for pain and screw loosening after a mean of 2.86 years (1.9-5.3 years). Optical microscopy and scanning electron microscopy were used to evaluate wear, deformation and surface damage, and attenuated total reflectance Fourier transform infrared spectroscopy to assess surface chemical composition of the spacers. Periprosthetic tissue morphology and wear debris were determined using light microscopy, and PCU and PET wear debris by polarized light microscopy. RESULTS All implants had surface damage on the PCU spacers consistent with scratches and plastic deformation; 3 of 5 exhibited abrasive wear zones. In addition to fraying of the outer fibers of the PET cords in five implants, one case also evidenced cord fracture. The pedicle screws were unremarkable. Patient periprosthetic tissues around the three implants with visible PCU damage contained wear debris and a corresponding macrophage infiltration. For the patient revised for cord fracture, the tissues also contained large wear particles (>10 μm) and giant cells. Tissues from the other two patients showed comparable morphologies consisting of dense fibrous tissue with no inflammation or wear debris. CONCLUSIONS This is the first study to evaluate wear accumulation and local tissue responses for explanted Dynesys(®) devices. Polymer wear debris and an associated foreign-body macrophage response were observed in three of five cases.

Energy Analysis of Bare Electrodynamic Tethers

The design of an electrodynamic tether is a complex task that involves the control of dynamic instabilities, optimization of the generated power (or the descent time in deorbiting missions), and minimization of the tether mass. The electrodynamic forces on an electrodynamic tether are responsible for variations in the mechanical energy of the tethered system and can also drive the system to dynamic instability. Energy sources and sinks in this system include the following: 1) ionospheric impedance, 2) the potential drop at the cathodic contactor, 3) ohmic losses in the tether, 4) the corotational plasma electric field, and 5) generated power and/or 6) input power. The analysis of each of these energy components, or bricks, establishes parameters that are useful tools for tether design. In this study, the nondimensional parameters that govern the orbital energy variation, dynamic instability, and power generation were characterized, and their mutual interdependence was established. A space-debris mitigation mission was taken as an example of this approach for the assessment of tether performance. Numerical simulations using a dumbbell model for tether dynamics, the International Geomagnetic Reference Field for the geomagnetic field, and the International Reference Ionosphere for the ionosphere were performed to test the analytical approach. The results obtained herein stress the close relationships that exist among the velocity of descent, dynamic stability, and generated power. An optimal tether design requires a detailed tradeoff among these performances in a real-world scenario.

Analysis of Proseds bare-tether performance

NASA's tether experiment ProSEDS will be placed in orbit on board a Delta-II rocket in early 2003. ProSEDS will test bare-tether electron collection, deorbiting of the rocket second stage, and the system dynamic stability. ProSEDS performance will vary both because ambient conditions change along the orbit and because tether-circuit parameters follow a step by step sequence in the current operating cycle. In this work we discuss how measurements of tether current and bias, plasma density, and deorbiting rate can be used to check the OML law for current collection. We review circuit bulk elements; characteristic lengths and energies that determine collection (tether radius, electron thermal gyroradius and Debye length, particle temperatures, tether bias, ion ram energy); and lengths determining current and bias profiles along the tether (extent of magnetic self-field, a length gauging ohmic versus collection impedances, tether length). The analysis serves the purpose of estimating ProSEDS behavior in orbit and fostering our ability for extrapolating ProSEDS flight data to different tether and environmental conditions.

The dynamics of axisymmetric slender liquid bridges between unequal disks

n this paper the influence of an axial microgravity on the dynamic stability of axisymmetric slender liquid bridges between unequal disks is numerically studied by using a one-dimensional theory. The breaking of such liquid configurations is analyzed and the dependence of some overall characteristics of the breaking process on the value of axial microgravity, the geometry and the volume of the liquid bridge, as well as stability limits are obtained.