A note about the appearance of non-hyperbolic solutions in a mechanical pendulum system

The investigation of the behavior of a nonlinear system consists in the analysis of different stages of its motion, where the complexity varies with the proximity of a resonance region. Near this region the stability domain of the system undergoes sudden changes due basically to competition and interaction between periodic and saddle solutions inside the phase portrait, leading to the occurrence of the most different phenomena. Depending of the domain of the chosen control parameter, these events can reveal interesting geometric features of the system so that the phase portrait is not capable to express all them, since the projection of these solutions on the two-dimensional surface can hide some aspects of these events. In this work we will investigate the numerical solutions of a particular pendulum system close to a secondary resonance region, where we vary the control parameter in a restrict domain in order to draw a preliminary identification about what happens with this system. This domain includes the appearance of non-hyperbolic solutions where the basin of attraction in the center of the phase portrait diminishes considerably, almost disappearing, and afterwards its size increases with the direction of motion inverted. This phenomenon delimits a boundary between low and high frequency of the external excitation.

Dynamics of vibrating systems with tuned liquid column dampers and limited power supply

Tuned liquid column dampers are U-tubes filled with some liquid, acting as an active vibration damper in structures of engineering interest like buildings and bridges. We study the effect of a tuned liquid column damper in a vibrating system consisting of a cart which vibrates under driving by a source with limited power supply (non-ideal excitation). The effect of a liquid damper is studied in some dynamical regimes characterized by coexistence of both periodic and chaotic motion. (c) 2005 Elsevier Ltd. All rights reserved.

Some aspects of the dynamics of fictitious Earth's satellites

In this work we study the dynamics of fictitious satellites of the Earth. In the first part we do not consider the effect of the Moon and study the dynamics in the restrict three-body model, i.e., a massless satellite under the effect of the gravitational force of an oblate Earth and that of the Sun. We show that a satellite starting with an almost circular orbit suffers very large variations of eccentricity, depending on the initial inclination of the orbit with respect to the reference plane. As the eccentricity may be driven to very large values (approximate to0.9) mutual collisions between satellites or collisions with the planet may occur. In the second part, we include the gravitational effect of the Moon. In this case, we find two regions with large variations of eccentricity due to the presence of the Moon. Consequently, in both scenarios, we find some large regions of the phase space where the long-term stability of some fictitious Earth's satellites is not possible. (C) 2001 Elsevier B.V. Ltd. 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 non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

On an Active Control for a Structurally Nonlinear Mechanical System, Taking Into Account an Energy Pumping

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

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

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

Scaling dynamics for a particle in a time-dependent potential well

Some dynamical properties for a classical particle confined in an infinitely deep box of potential containing a periodically oscillating square well are studied. The dynamics of the system is described by using a two-dimensional non-linear area-preserving map for the variables energy and time. The phase space is mixed and the chaotic sea is described using scaling arguments. Scaling exponents are obtained as a function of all the control parameters, extending the previous results obtained in the literature. (c) 2012 Elsevier B.V. All rights reserved.

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

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

Instability zones for satellites of asteroids: The example of the (87) Sylvia system

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

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

On a nonlinear and chaotic non-ideal vibrating system with shape memory alloy (SMA)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The dynamics of a one-dimensional parabolic problem versus the dynamics of its discretization

In this paper we prove that the spatial discretization of a one dimensional system of parabolic equations. with suitably small step size, contains exactly the same asymptotic dynamics as the continuous problem. (C) 2000 Academic Press.

Dynamics and cytochemistry of oogenesis in Leporinus striatus Kner (Teleostei, Characiformes, Anostomidae) from the Rio Sapucaí, Minas Gerais State, Brazil

Oogenesis involves a sequense of transformations which are undergone by female germ cells. These cells change into oogonias and then into mature oocytes. Sexually mature females were collected monthly, during one year, from the Rio Sapucaí, tributary of the Rio Grande, which is part of the Furnas Reservoir system in the state of Minas Gerais. The observed material showed that oogonias were small spherical cells, had a big spherical nucleus, with a single nucleolus, and weakly stained cytoplasm with eosinophilic granules (FG stained), which indicate their protein content. The primary oocytes showed a big basophilic nucleus, with a large peripheral nucleolus, and several smaller nucleoli. They show a reduced cytoplasmic content. The previtellogenic oocytes presented voluminous cytoplasm and nucleus with several small peripheral nucleoli. The oocytes underwent vitellogenesis with the development of the zona radiata and the follicle cells. The zona radiata had two layers, the outer and the inner, which showed its protein content when stained with CM and FG techniques. TB pH 2.5 and pH 4.0 staining showed that oocytes undergoing vitellogenesis presented weakly stained cytoplasm and peripheral cytoplasmic vesicles. The follicle cells that were squamous became cuboidal. In mature oocytes, the yolk granules that filled the cytoplasm became green and blue when stained with FG and CM techniques, indicating their protein content. The perivitclline region showed rosy stained vesicles (TB pH 2.5 and pH 4.0) spread among the weakly stained peripheral vesicles, which seemed to be the cortical alveoli. The zona radiata cells, CM and FG stained, still showed two layers like the oocytes from the previous stage, but thicker.