Limit sets and the Poincare-Bendixson Theorem in impulsive semidynamical systems

We consider semidynamical systems with impulse effects at variable times and we discuss some properties of the limit sets of orbits of these systems such as invariancy, compactness and connectedness. As a consequence we obtain a version of the Poincare-Bendixson Theorem for impulsive semidynamical systems. (C) 2008 Elsevier Inc. All rights reserved.

Opinion dynamics of learning agents: does seeking consensus lead to disagreement?

We study opinion dynamics in a population of interacting adaptive agents voting on a set of issues represented by vectors. We consider agents who can classify issues into one of two categories and can arrive at their opinions using an adaptive algorithm. Adaptation comes from learning and the information for the learning process comes from interacting with other neighboring agents and trying to change the internal state in order to concur with their opinions. The change in the internal state is driven by the information contained in the issue and in the opinion of the other agent. We present results in a simple yet rich context where each agent uses a Boolean perceptron to state their opinion. If the update occurs with information asynchronously exchanged among pairs of agents, then the typical case, if the number of issues is kept small, is the evolution into a society torn by the emergence of factions with extreme opposite beliefs. This occurs even when seeking consensus with agents with opposite opinions. If the number of issues is large, the dynamics becomes trapped, the society does not evolve into factions and a distribution of moderate opinions is observed. The synchronous case is technically simpler and is studied by formulating the problem in terms of differential equations that describe the evolution of order parameters that measure the consensus between pairs of agents. We show that for a large number of issues and unidirectional information flow, global consensus is a fixed point; however, the approach to this consensus is glassy for large societies.

A Higher order and stable method for the numerical integration of Random Differential Equations

Trabalho apresentado no Congresso Nacional de Matemática Aplicada à Indústria, 18 a 21 de novembro de 2014, Caldas Novas - Goiás

Spatial variability of soil physical properties in two management systems in sugarcane crop

O objetivo deste trabalho foi caracterizar a variabilidade espacial da densidade do solo (Ds), teor de água no solo (θ) e porosidade total (Pt) em dois sistemas de manejo da colheita da cana-de-açúcar, com queima e sem queima, em um Latossolo Vermelho, na camada de 0-0,20 m. A área de estudo está localizada no município de Rio Brilhante-MS, na Usina Eldorado. A parcela de cada talhão apresentou malha com comprimento de 180 m e largura de 145,6 m, perfazendo 90 pontos distribuídos na forma de uma grade de nove colunas por dez linhas, com pontos distanciados 20 m de seu vizinho. Foram coletadas amostras de solo na camada de 0-0,20 m, nos anos agrícolas de 2007/2008 e 2008/2009. O sistema de colheita com queima apresentou maior densidade em relação ao mecanizado, nos dois períodos de análise. O teor de água no solo, assim como a porosidade, teve aumento proporcional com relação à diminuição da densidade do sistema de colheita com queima para com o mecanizado.

Effects of different soil tillage systems and coverages on soybean crop in the Botucatu Region in Brazil

Nowadays, agricultural practices should combine high yields with a sustainable use of resources. Different tillage practices and crop covers, if combined, may help to achieve both objectives. In this work, several traits of a soybean (Glycine max L. Merr) cultivar were studied under different conditions of tillage and previous soil coverages. The experiment was installed at Lageado Research Station, Botucatu county, SP, Brazil, on a Paleudult. It consisted of nine treatments (combining three systems of soil tillage and three cover crops) and 4 replicates, yielding 36 plots of a randomized block experimental design. The soil tillage systems considered were: (i) conventional tillage with two heavy harrowing and a levelling harrowing; (ii) chiseling, and (iii) no-tillage with chemical drying of vegetation. The three cover crops used were: black oat, sorghum and spontaneous vegetation. Analyzed variables were: plant height, initial and final plant densities, height of first pod insertion, weight of a thousand grains, number of pods per plant, number of grains per pod, and crop yield. No significant differences were observed for most of the analyzed variables; however, conventional tillage produced significantly heavier grains and a higher number of pods per plant. The selected covers were considered an excellent coverage prior to planting soybean in a crop rotation. The three tillage systems can be used for deployment of culture without compromising the development of soybean.

Estudo e implementação de um controlador preditivo generalizado bilinear compensado adaptativo

The present work presents the study and implementation of an adaptive bilinear compensated generalized predictive controller. This work uses conventional techniques of predictive control and includes techniques of adaptive control for better results. In order to solve control problems frequently found in the chemical industry, bilinear models are considered to represent the dynamics of the studied systems. Bilinear models are simpler than general nonlinear model, however it can to represent the intrinsic not-linearities of industrial processes. The linearization of the model, by the approach to time step quasilinear , is used to allow the application of the equations of the generalized predictive controller (GPC). Such linearization, however, generates an error of prediction, which is minimized through a compensation term. The term in study is implemented in an adaptive form, due to the nonlinear relationship between the input signal and the prediction error.Simulation results show the efficiency of adaptive predictive bilinear controller in comparison with the conventional.

Alginate-chitosan systems: In vitro controlled release of triamcinolone and in vivo gastrointestinal transit

The aim of this study was to develop multiparticulate therapeutic systems of alginate (AL) and chitosan (CS) containing triamcinolone (TC) to colonic drug delivery. Multiparticulate systems of AL-CS, prepared by a complex coacervation/ionotropic gelation method, were characterized for morphological and size aspects, swelling degree, encapsulation content and efficiency, in vitro release profile in different environments simulating the gastrointestinal tract (GIT) and in vivo gastrointestinal transit. The systems showed suitable morphological characteristics with particle diameters of approximately 1.6 mm. In simulated gastric environment, at pH 1.2, the capsules presented low degree of swelling and in vitro release of drug. A higher swelling degree was observed in simulated enteric environment, pH 7.5, followed by erosion. Practically all the drug was released after 6 h of in vitro assay. The in vivo analysis of gastrointestinal transit, carried out in rats, showed that the systems passed practically intact through the stomach and did not show the same profile of swelling observed in the in vitro tests. It was possible to verify the presence of capsules in the colonic region of GIT. The results indicate that AL-CS multiparticulate systems can be used as an adjuvant for the preparation of therapeutic systems to colonic delivery of drugs. (C) 2010 Elsevier Ltd. All rights reserved.

General solutions for some classes of interacting two field kinks

In this work we present some classes of models whose the corresponding two coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. In these cases the so-called trial orbit method is completely unnecessary. We recall that some physically important models as, for instance, the problem of tiling a plane with a network of defects and polymer properties are in this class of models. (c) 2005 Elsevier B.V. All rights reserved.

Signal-flow graphs: Direct method of reduction and MATLAB implementation

Block diagrams and signal-flow graphs are used to represent and to obtain the transfer function of interconnected systems. The reduction of signal-flow graphs is considered simpler than the reduction of block diagrams for systems with complex interrelationships. Signal-flow graphs reduction can be made without graphic manipulations of diagrams, and it is attractive for a computational implementation. In this paper the authors propose a computational method for direct reduction of signal-flow graphs. This method uses results presented in this paper about the calculation of literal determinants without symbolic mathematics tools. The Cramer's rule is applied for the solution of a set of linear equations, A program in MATLAB language for reduction of signal-flow graphs with the proposed method is presented.

Mitigation of symmetry condition in positive realness for adaptive control

Feasibility of nonlinear and adaptive control methodologies in multivariable linear time-invariant systems with state-space realization (A, B, C) is apparently limited by the standard strictly positive realness conditions that imply that the product CB must be positive definite symmetric. This paper expands the applicability of the strictly positive realness conditions used for the proofs of stability of adaptive control or control with uncertainty by showing that the not necessarily symmetric CB is only required to have a diagonal Jordan form and positive eigenvalues. The paper also shows that under the new condition any minimum-phase systems can be made strictly positive real via constant output feedback. The paper illustrates the usefulness of these extended properties with an adaptive control example. (C) 2006 Elsevier Ltd. All rights reserved.

Nonlinear methods of heart rate variability analysis in diabetes

Background: The autonomic dysfunction stands out among the complications associated to diabetes mellitus (DM) and may be evaluated through the heart rate variability (HRV), a noninvasive tool to investigate the autonomic nervous system that provides information of health impairments and may be analyzed by using linear and nonlinear methods. Several studies have shown that HRV measured in a linear form is altered in DM. Nevertheless, a few studies investigate the nonlinear behavior of HRV. Therefore, this study aims at gathering information regarding the autonomic changes in subjects with DM identified by nonlinear analysis of HRV.Methods: For that, searches were performed on Medline, SciELO, Lilacs and Cochrane databases using the crossing between the key-words: diabetic autonomic neuropathy, autonomic nervous system, diabetes mellitus and heart rate variability. As inclusion criteria, articles published on a period from 2000 to 2010 with DM type land type II population which assessed the autonomic nervous system by nonlinear indices HRV were considered.Results: The electronic search resulted in a total of 1873 references with the exclusion of 1623 titles and abstracts and from the 250 abstracts remaining, 8 studies were selected to the final analysis that completed the inclusion criteria.Conclusions: In general, the analysis showed that the nonlinear techniques of HRV allowed detecting autonomic changes in DM. The methods of nonlinear analysis are indicated as a possible tool to be used for early diagnosis and prognosis of autonomic dysfunction in DM.

Photoelastic Analysis of Stress Distribution in Different Retention Systems for Facial Prosthesis

The aim of this study was to assess the behavior and stress distribution of 3 retention systems associated with implant for facial prosthesis by using the photoelasticity method. A photoelastic model was made from the replica of the orbital region on the left side of a dry skull with two 4-mm implants fixed in the superior orbital region. Three facial prosthetic retention systems were made for this study: O'ring, bar-clip, and magnets. The set (model/retention systems/prosthesis) was placed in a polariscope, and then traction began to be applied to the retention systems. The limit values for removal of the retention system were obtained by tests performed in an EMIC Universal test machine. The results were obtained by observation during the experiments and by photographic record of the stress behavior in the photoelastic model, resulting from the traction of the retention systems. In the magnet system, a lowest formation of fringes was verified both around and between the implants; in the O'ring system, the formation of photoelastic fringes was noted between the implants in the apical region; and in the bar-clip system, there was a greater concentration of colored fringes in the regions between the implants and cervical area. Based on the results obtained, it was concluded that the retention systems produced different stress distribution characteristics that, in general, were concentrated in the area around the implants, and the highest concentration of fringes, in increasing order, occurred ill the retention systems of the magnets, O'ring, and bar-clip.

Integral equations of scattering in one dimension

A self-contained discussion of integral equations of scattering is presented in the case of centrally symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and three dimensions. The present discussion illustrates in a simple fashion the concept of partial-wave decomposition, Green's function, Lippmann-Schwinger integral equations of scattering for wave function and transition operator, optical theorem, and unitarity relation. We illustrate the present approach with a Dirac delta potential. (C) 2001 American Association of Physics Teachers.

Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa-Holm equation

In this Letter we investigate Lie symmetries of a (2 + 1)-dimensional integrable generalization of the Camassa-Holm (CH) equation. Through the similarity reductions we obtain four different (1 + 1)-dimensional systems of partial differential equations in which one of them turns out to be a (1 + 1)-dimensional CH equation. We establish their integrability by providing the Lax pair for all of them. Further, we present a brief analysis for some types of particular solutions which include the cuspon, peakon and soliton solutions for the two-dimensional generalization of the CH equation. (C) 2000 Published by Elsevier B.V. B.V.

Homoclinic bifurcations in reversible Hamiltonian systems

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u(iv) + au - u +f(u, b) = 0 as a model, where fis an analytic function and a, b real parameters. These equations are important in several physical situations such as solitons and in the existence of finite energy stationary states of partial differential equations, but no assumptions of any kind of discrete symmetry is made and the analysis here developed can be extended to others Hamiltonian systems and successfully employed in situations where standard methods fail. We reduce the problem of computing these orbits to that of finding the intersection of the unstable manifold with a suitable set and then apply it to concrete situations. We also plot the homoclinic values configuration in parameters space, giving a picture of the structural distribution and a geometrical view of homoclinic bifurcations. (c) 2005 Published by Elsevier B.V.