On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.

Degenerate hope bifurcations in Chua's system

In this paper we study the local codimension one, two and three Hopf bifurcations which occur in the classical Chua's differential equations with cubic nonlinearity. A detailed analytical description of the regions in the parameter space for which multiple small periodic solutions bifurcate from the equilibria of the system is obtained. As a consequence, a complete answer for the challenge proposed in [Moiola & Chua, 1999] is provided. © 2009 World Scientific Publishing Company.

Swarm control designs applied to a micro-electro-mechanical gyroscope system (MEMS)

This paper analyzes the non-linear dynamics of a MEMS Gyroscope system, modeled with a proof mass constrained to move in a plane with two resonant modes, which are nominally orthogonal. The two modes are ideally coupled only by the rotation of the gyro about the plane's normal vector. We demonstrated that this model has an unstable behavior. Control problems consist of attempts to stabilize a system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. We also developed a particle swarm optimization technique for reducing the oscillatory movement of the nonlinear system to a periodic orbit. © 2010 Springer-Verlag.

Predatory behavior of Canthon virens (Coleoptera: Scarabaeidae): A predator of leafcutter ants

We present a detailed description of the predatory behavior of the beetle Canthon virens Mannerheim, 1829, on the leafcutter ant Atta sp. We observed 51 acts of predation, which were also recorded on film and subjected to behavioral analysis. Canthon virens exhibited 28 behaviors while predating upon Atta sp. queens. Adult beetles search for queens while flying in a zigzag pattern, 15 to 20cm above the ground. After catching a queen, the predator stands on its back and starts cutting the queen cervix. Once the prey is decapitated, the predator rolls it until an insurmountable obstacle is reached. The distance from the site of predation to the obstacle can vary widely and is unpredictable. The beetle rolling the queen also buries it in a very peculiar way: first, it digs a small hole and pulls the queen inside, while another beetle is attached to the prey. The burial process takes many hours (up to 12) and may depend on the hardness of the soil and the presence of obstacles. In general, one or two beetles are found in a chamber with the queen after it is buried. They make the brood balls, which serve as food for the offspring. This study contributes to the knowledge of the predatory behavior of Canthon virens, a predator poorly studied in Brazil and widespread in the country. Copyright © 2012 Luiz Carlos Forti et al.

Insect/Bt-cotton interactions: Are immunological variables and hemocyte ultrastructure in Podisus nigrispinus (Hemiptera: Pentatomidae) affected?

Recent studies have shown that ingestion by the army worm Spodoptera frugiperda of Cry1Ac toxin from Bt cotton promotes histochemical and ultrastructural changes in the digestive cells of the predatory pentatomid bug Podisus nigrispinus. Therefore, mindful of the changes in the midgut of the predator, which represents the first line of defence in this insect, our aim was to test the hypothesis that the consumption of Bt cotton-fed S. frugiperda by P. nigrispinus might lead to alterations in components of the immune system of P. nigrispinus. The Cry1Ac toxin level in the leaves of Bt cotton, nitric oxide, phenoloxidase activity, and total proteins were quantified by ELISA. Total and differential hemocyte counts were evaluated, and hemocyte ultrastructure analysis was undertaken. We found that ingestion of the prey fed daily with approximately 23 ± 0.70 ng g-1 Cry1Ac by wet weight of leaves, and expressed by the Bt cotton, induces small ultrastructural changes in the predator's granulocytes and plasmatocytes. However, these changes did not affect the total number and differential and humoral variables analyzed for the bug's hemocytes. © 2013 Copyright Taylor and Francis Group, LLC.

Optimal linear control to parametric uncertainties in a micro electro mechanical system

This paper, a micro-electro-mechanical systems (MEMS) with parametric uncertainties is considered. The non-linear dynamics in MEMS system is demonstrated with a chaotic behavior. We present the linear optimal control technique for reducing the chaotic movement of the micro-electromechanical system with parametric uncertainties to a small periodic orbit. The simulation results show the identification by linear optimal control is very effective. © 2013 Academic Publications, Ltd.

Hydrostatic and [001] uniaxial pressure on anatase TiO2 by periodic B3LYP-D* calculations

The effect of high hydrostatic and [001] uniaxial pressures on TiO 2 anatase was studied under the framework of periodic calculations with the inclusion of DFT-D2 dispersion potential adjusted for this system (B3LYP-D*). The role of dispersion in distorted unit cells was evaluated in terms of lattice parameters, elastic constants, equation of state, vibrational properties, and electronic properties (band structure and density of states). A more reliable description at high pressures was achieved because the B3LYP-D* presented an improvement in all properties for undistorted bulk over conventional B3LYP and B3LYP-D. From density of states analysis, we observed that the contribution of crystalline orbitals to the edge of valence and conduction bands changed within applied pressure. The studied distortions can give some insight into behavior of electronic and structural properties due to local stress in anatase bulk from doping, defects, and physical tensions in nanometric forms. © 2013 American Chemical Society.

Predation-risk effects of predator identity on the foraging behaviors of frugivorous bats

Predators directly and indirectly affect the density and the behavior of prey. These effects may potentially cascade down to lower trophic levels. In this study, we tested the effects of predator calls (playbacks of bird vocalizations: Tyto alba, Speotyto cunicularia, and Vanellus chilensis), predator visual stimuli (stuffed birds) and interactions of visual and auditory cues, on the behavior of frugivore phyllostomid bats in the field. In addition, we tested if the effects of predation risk cascade down to other trophic levels by measuring rates of seed dispersal of the tree Muntingia calabura. Using video recording, we found that bats significantly decreased the foraging frequency on trees when a visual cue of T. alba was present. However, no stimuli of potential predatory birds, including vocalization of T. alba, affected bat foraging frequency. There was a change in bat behavior during 7 min, but then their frequency of activity gradually increased. Consequently, the presence of T. alba decreased by up to ten times the rate of seed removal. These results indicate that risk sensitivity of frugivorous phyllostomid bats depends on predator identity and presence. Among the predators used in this study, only T. alba is an effective bat predator in the Neotropics. Sound stimuli of T. alba seem not to be a cue of predation risk, possibly because their vocalizations are used only for intraspecific communication. This study emphasizes the importance of evaluating different predator stimuli on the behavior of vertebrates, as well as the effects of these stimuli on trait-mediated trophic cascades. © 2013 Springer-Verlag Berlin Heidelberg.

Critical currents and melting temperature of a two-dimensional vortex lattice with periodic pinning

The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two-dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagomé pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength. © 2012 Springer Science+Business Media New York.

Control design applied to a non-ideal structural system with behavior chaotic

In this paper we study the behavior of a structure vulnerable to excessive vibrations caused by an non-ideal power source. To perform this study, the mathematical model is proposed, derive the equations of motion for a simple plane frame excited by an unbalanced rotating machine with limited power (non-ideal motor). The non-linear and non-ideal dynamics in system is demonstrated with a chaotic behavior. We use a State-Dependent Riccati Equation Control technique for regulate the chaotic behavior, in order to obtain a periodic orbit small and to decrease its amplitude. The simulation results show the identification by State-Dependent Riccati Equation Control is very effective. © 2013 Academic Publications, Ltd.

Damage detection in nonlinear structures using discrete-time volterra series

Structural damage identification is basically a nonlinear phenomenon; however, nonlinear procedures are not used currently in practical applications due to the complexity and difficulty for implementation of such techniques. Therefore, the development of techniques that consider the nonlinear behavior of structures for damage detection is a research of major importance since nonlinear dynamical effects can be erroneously treated as damage in the structure by classical metrics. This paper proposes the discrete-time Volterra series for modeling the nonlinear convolution between the input and output signals in a benchmark nonlinear system. The prediction error of the model in an unknown structural condition is compared with the values of the reference structure in healthy condition for evaluating the method of damage detection. Since the Volterra series separate the response of the system in linear and nonlinear contributions, these indexes are used to show the importance of considering the nonlinear behavior of the structure. The paper concludes pointing out the main advantages and drawbacks of this damage detection methodology. © (2013) Trans Tech Publications.

Theoretical perspectives on the dynamics of communities with intraguild predation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Application of passive control to energy harvester efficiency using a nonideal portal frame structural support system

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

Identification of nonlinear structures using discrete-time Volterra series

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

Zero, minimum and maximum relative radial acceleration for planar formation flight dynamics near triangular libration points in the Earth-Moon system

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