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A histological and morphometric analysis of the Dorsal Root Ganglia (DRGs) and their sensorial neurons were carried out to contribute to the understanding of how do their nervous system adapt to their fast body growth. Two age group of fish (age 1 = 20 dph; age 2 = 30 dph), and three spinal sections were used (anterior, middle, and posterior). Histologically, the DRGs and their sensorial neurons are similar to those described for mammals, birds, amphibians, and reptiles. On the other hand, the DRGs and their neurons are larger in age group 2 fish compared with age group 1 fish. There were also differences in the DRGs spinal sections in volume and number of neurons, and the sensorial neurons differed in area. The distribution of the types A and B subpopulations was 36 and 64%, respectively for age group 1 fish; and 25 and 75%, respectively for age group 2 fish. The differences between the DRGs and their sensorial neurons can be attributed to the proportion of target tissue (muscular, cutaneous, and visceral) that each of the DRGs and their neurons must innervate depending on their location. In these species, even a small increment in body mass, represents a change in DRGs and their sensory neurons, suggesting that White Cachama is a good model for the study of the adaptation of the nervous system to large changes in body size.Se realizó un análisis histológico y morfométrico de los Ganglios de la Raíz Dorsal (GRD) y sus neuronas sensoriales, para contribuir al entendimiento de cómo el sistema nervioso se adapta al rápido incremento en el tamaño corporal. Se utilizaron peces en dos clases de edad (edad 1 = 20 dph; edad 2 = 30 dph), y se tomaron GRD de tres secciones de la espina del pez (anterior, medio y posterior). Histológicamente, los GRDs son similares a los de mamíferos, aves, anfibios y reptiles. Los GRDs y sus neuronas son de mayor tamaño en los peces del grupo de edad 2. Se presentaron diferencias en el volumen de los GRDs al igual que en el número y área neuronal en los diferentes niveles espinales. También la ubicación de los GRD influye en el tamaño de los ganglios, y el número y tamaño de las neuronas. Las neuronas tipos A y B representan el 36 y 64%, respectivamente para los peces del grupo de edad 1; y 25 y 75%, respectivamente para los peces del grupo de edad 2. Estas diferencias pueden atribuirse a sus eferentes y a la proporción de tejido blanco (muscular, cutáneo o visceral) que cada GRD y sus neuronas debe inervar dependiendo de su ubicación anatómica. En esta especie, un pequeño incremento en masa corporal representa un cambio importante en los GRD y sus neuronas sensoriales, sugiriendo que la ''cachama blanca'' es un buen modelo para el estudio de la adaptación del sistema nervioso a grandes cambios en tamaño corporal.

For magnetically confined plasmas in tokamaks, we have numerically investigated how Lagrangian chaos at the plasma edge affects the plasma confinement. Initially, we have considered the chaotic motion of particles in an equilibrium electric field with a monotonic radial profile perturbed by drift waves. We have showed that an effective transport barrier may be created at the plasma edge by modifying the electric field radial profile. In the second place, we have obtained escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall with resonant modes due to the action of an ergodic magnetic limiter. For monotonic plasma current density profiles we have obtained distributions of field line connections to the wall and line escape channels with the same spatial pattern as the magnetic footprints on the tokamak walls.

We show a scenario of a two-frequency torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T 2 with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-II intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. � 2007 Elsevier Ltd. All rights reserved.

We present a computational procedure to control an experimental chaotic system by applying the occasional proportional feedback (OPF) method. The method implementation uses the fuzzy theory to relate the variable correction to the necessary adjustment in the control parameter. As an application we control the chaotic attractors of the Chua circuit. We present the developed circuits and algorithms to implement this control in real time. To simplify the used procedure, we use a low resolution analog to digital converter compensated for a lowpass filter that facilitates similar applications to control other systems.

We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on–off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable.

The dynamics of a dissipative vibro-impact system called impact-pair is investigated. This system is similar to Fermi-Ulam accelerator model and consists of an oscillating one-dimensional box containing a point mass moving freely between successive inelastic collisions with the rigid walls of the box. In our numerical simulations, we observed multistable regimes, for which the corresponding basins of attraction present a quite complicated structure with smooth boundary. In addition, we characterize the system in a two-dimensional parameter space by using the largest Lyapunov exponents, identifying self-similar periodic sets.

Piaractus brachypomus es una especie de gran importancia económica en colombia. el propósito de este trabajo fue efectuar un análisis de la hipófisis de alevinos de esta especie a nivel histológico y anatómico. Se realizaron cortes sagitales y transversales de 5 y 7 µm de las hipófisis de veinte alevinos, para estudios histológico y de reconstrucción tridimensional. En los alevinos, la hipófisis se ubica en la zona ventral del cerebro, posterior al quiasma óptico, parcialmente integrada entre el nucleus tuberalis ventralis (TV) y el hypotalamus periventriculares caudalis (Hc) del hipotálamo, la que parece estar conectada por tejidos conectivo y nervioso. La hipófisis presenta células basófilas (B) con núcleos grandes y excéntricos, y cromófobas (C) con núcleos pequeños y un citoplasma sin tinción, no hay presencia de acidófilas (A). La irrigación sanguínea está presente en todas las zonas de la hipófisis. Las diferencias con la literatura son atribuidas a la inmadurez de la glándula.Piaractus brachypomus is a species of great economic importance in Colombia. The purpose of this study is to accomplish an analysis at the histological and anatomical level of alevin pituitary of this species. We realized sagittal and transversal cuts of 5 and 7 µm of 20 alevin pituitaries for a histological and three-dimensional reconstruction studies. The pituitary of these specific alevins is located in the ventral zone of the brain, posterior to the optic chiasm, partially integrated by connective and nervous tissues between the nucleus tuberalis ventralis (TV) and hypotalamus periventriculares caudalis (Hc). The pituitary contains basophils with large and non-centric nuclei, as well as chromophobes (C) with small nuclei and unstained cytoplasm. There is no presence of acidophils (A); however, blood flow reaches all parts of the pituitary. Discrepancies between our study and that of literature are attributed to glandular immaturity.

The magnetic field line structure in a tokamak can be obtained by direct numerical integration of the field line equations. However, this is a lengthy procedure and the analysis of the solution may be very time-consuming. Otherwise we can use simple two-dimensional, area-preserving maps, obtained either by approximations of the magnetic field line equations, or from dynamical considerations. These maps can be quickly iterated, furnishing solutions that mirror the ones obtained from direct numerical integration, and which are useful when long-term studies of field line behavior are necessary (e.g. in diffusion calculations). In this work we focus on a set of simple tokamak maps for which these advantages are specially pronounced.

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing.

We have investigated plasma turbulence at the edge of a tokamak plasma using data from electrostatic potential fluctuations measured in the Brazilian tokamak TCABR. Recurrence quantification analysis has been used to provide diagnostics of the deterministic content of the series. We have focused our analysis on the radial dependence of potential fluctuations and their characterization by recurrence-based diagnostics. Our main result is that the deterministic content of the experimental signals is most pronounced at the external part of the plasma column just before the plasma radius. Since the chaoticity of the signals follows the same trend, we have concluded that the electrostatic plasma turbulence at the tokamak plasma edge can be partially explained by means of a deterministic nonlinear system.

Two reproducible regimes of tokamak operation, with excitation or suppression of MHD activity can be obtained using a voltage-biased electrode inside the edge of the TCABR tokamak. The experiment was carried out adjusting the tokamak parameters to obtain two types of discharges: with strong or weak MHD activity, without biasing in both cases. The plasma current was adjusted to cover a range of safety factor from 2.9 up to 3.5, so that when biasing was applied the magnetic island (3,1) could interact with the edge barrier. The application of biasing in subsequent discharges of each type resulted in excitation or suppression of the MHD activity. The results show that the dominant modes are m = 2, n = 1 and m = 3, n = 1 for excitation and partial suppression, respectively. In both regimes a strong decrease in the radial electric field is detected with destruction of the transport barrier and of the improved confinement caused by different mechanisms. The measurements include temporal behaviour of edge transport, turbulence, poloidal electric and magnetic fields, edge density, radial electric fields and radial profile of Hα line intensity. The explanation of the excitation and suppression processes is discussed in the paper.

We considered a coupled chaotic logistic map lattice exhibiting the scale-free property: the outreach connectivity of each node obeys a power-law distribution. We analyzed a weak form of coherent spatio-temporal behavior (direction coherence) which presents features common to completely synchronized states, like a transitional behavior with intermittent bursting. We studied such phenomena and their dependence on the parameters of the coupled scale-free lattice. Prospective applications in neuronal networks are emphasized.

The influence of an ergodic magnetic limiter (EML) on plasma turbulence is investigated in the Tokamak Chauffage Alfvén Brésilien (TCABR), a tokamak with a peculiar natural superposition of the electrostatic and magnetic fluctuation power spectra. Experimental results show that the EML perturbation can reduce both the magnetic oscillation and the electrostatic plasma turbulence. Whenever this occurs, the turbulence-driven particle transport is also reduced. Moreover, a bispectral analysis shows that the nonlinear coupling between low- and high-frequency electrostatic fluctuations increases significantly with the EML application.

The magnetic field line structure of tokamaks with reversed magnetic shear is analyzed by means of a nontwist map model that takes into account non-integrable perturbations that describe ergodic magnetic limiters. The map studied possess behavior expected of the standard nontwist map, a well-studied map, despite the different symmetries and the existence of coupled perturbations. A distinguising feature of nontwist maps is the presence of good surfaces in the reveresed shear region, and consequently the appearance of a transport barrier inside the plasma. Such barriers are observed in the present model and are seen to be very robust. Very strong perturbations are required to destroy them, and even after breaking, the transport turns out to be diffusive. Poloidal diffusion is found to be two orders of magnitude higher than radial diffusion.

We apply a feedback control technique to suppress chaotic behavior in dissipative mechanical systems by using a small-amplitude damping signal. The control signal is obtained by varying the damping coefficient according to the velocity direction. As an application of this method, we present numerical simulations of an impact oscillator and the required damping law used to achieve the control. Our numerical results show the method effectiveness even for high levels of noisy perturbation.

The dynamics of vibro-impact systems of engineering interest is numerically studied by means of a prototype consisting of an oscillating cart containing a ball undergoing inelastic collisions with its walls. We have described a multistable regime, for which different attractors coexist with a complicated basin boundary structure in the phase space. We investigated the effect of adding a certain amount of parametric noise in this model, focusing on the basin hopping, i.e., the intermittent switching between basins of different attractors. � 2005 Elsevier Ltd. All rights reserved.

We proposed a simple feedback control method to suppress chaotic behavior in oscillators with limited power supply. The small-amplitude controlling signal is applied directly to the power supply system, so as to alter the characteristic curve of the driving motor. Numerical results are presented showing the method efficiency for a wide range of control parameters. Moreover, we have found that, for some parameters, this kind of control may introduce coexisting periodic attractors with complex basins of attraction and, therefore, serious problems with predictability of the final state the system will asymptote to.

We characterized the influence of high period accelerator modes in the global dynamics of a non-dissipative Bouncer model . The dynamics of the system was investigated considering both complete and simplified approaches. Evaluating the average of the velocity over large ensembles of initial conditions for the complete mapping, we obtained particular ranges of the control parameter where high period accelerating structures are located. The position, influence and shape of the accelerator modes were obtained considering the symplectic mapping. Our results, lead us to infer that even for high period and less influent accelerator modes , the dynamics is globally affected for long time series, causing an anomalous diffusion , in compare with the regular Fermi acceleration .

Made available in DSpace on 2018-12-11T16:39:23Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-11-06 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two-dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the basins of the attracting fixed points is characterized, as we vary the control parameters. Crises between the attractors and their boundaries are observed. We found that the multiple attractors are intertwined, and when the boundary crisis between their stable and unstable manifolds occurs, it creates a successive mechanism of destruction for all attractors originated by the sinks. Also, a physical impact crisis is described, an important mechanism in the reduction of the number of attractors. Departamento de Física, UNESP, Universidade Estadual Paulista, Av. 24A, 1515, Bela Vista School of Mathematics, University of Bristol Instituto de Física, IFUSP, Universidade de São Paulo, USP, Cidade Universitária, Rua do Matão, Tr.R 187 Departamento de Física, UNESP, Universidade Estadual Paulista, Av. 24A, 1515, Bela Vista FAPESP: 2014/25316-3

Made available in DSpace on 2018-12-11T16:39:15Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-01-01 The transport and diffusion properties for the velocity of a Fermi-Ulam model were characterized using the decay rate of the survival probability. The system consists of an ensemble of noninteracting particles confined to move along and experience elastic collisions with two infinitely heavy walls. One is fixed, working as a returning mechanism of the colliding particles, while the other one moves periodically in time. The diffusion equation is solved, and the diffusion coefficient is numerically estimated by means of the averaged square velocity. Our results show remarkably good agreement of the theory and simulation for the chaotic sea below the first elliptic island in the phase space. From the decay rates of the survival probability, we obtained transport properties that can be extended to other nonlinear mappings, as well to billiard problems. Departamento de Fésica UNESP - Univ. Estadual Paulista, Ave. 24A, 1515, Bela Vista Instituto de Fésica IFUSP - Universidade de Sâo Paulo Cidade Universittéria, Rua do Matâo, Tr.R 187 School of Mathematics University of Bristol Abdus Salam International Center for Theoretical Physics, Strada Costiera 11 Departamento de Fésica UNESP - Univ. Estadual Paulista, Ave. 24A, 1515, Bela Vista

Ranking is an important task in information retrieval and has gained much attention in recent years. Among the most used strategies, machine learning has achieved important results. The current work proposes a new machine learning based ranking algorithm, the MLM-RANK. MLM-RANK is based on the recently proposed Minimal Learning Machine (MLM). MLM is a supervised learning method that requires the adjustment of a single hyper parameter. The proposed method was evaluated against Prank and ELM Rank, both state of the art point wise ranking methods. In these tests MLM-RANK achieved promising results.

Made available in DSpace on 2022-04-28T19:01:23Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-07-06 The ballistic increase for the velocity of a particle in a bouncing-ball model was investigated. The phenomenon is caused by accelerating structures in phase space known as accelerator modes. They lead to a regular and monotonic increase of the velocity. Here, both regular and ballistic Fermi acceleration coexist in the dynamics, leading the dynamics to two different growth regimes. We characterized deaccelerator modes in the dynamics, corresponding to unstable points in the antisymmetric position of the accelerator modes. In control parameter space, parameter sets for which these accelerations and deaccelerations constitute structures were obtained analytically. Since the mapping is not symplectic, we found fractal basins of influence for acceleration and deacceleration bounded by the stable and unstable manifolds, where the basins affect globally the average velocity of the system. Universidade Tecnológica Federal Do Paraná Instituto de Física, Universidade de São Paulo Departamento de Física, Universidade Estadual Paulista Abdus Salam International Center for Theoretical Physics, Strada Costiera 11 Departamento de Física, Universidade Estadual Paulista

A method for extracting finite-dimensional Hamiltonian systems from a class of 2+1 Hamiltonian mean field theories is presented. These theories possess noncanonical Poisson brackets, which normally resist Hamiltonian truncation, but a process of beatification by coordinate transformation near a reference state is described in order to perturbatively overcome this difficulty. Two examples of four-wave truncation of Euler's equation for scalar vortex dynamics are given and compared: one a direct non-Hamiltonian truncation of the equations of motion, the other obtained by beatifying the Poisson bracket and then truncating., Comment: 27 pages, 1 figure; references added

Analytical tokamak plasma equilibria, with non-monotonic plasma current profile and perturbed by ergodic magnetic limiters, are described by non-twist conservative maps. Examples are given of concentration of magnetic field lines escaping to the tokamak wall. The robustness of invariant curves on the shearless region is also observed.

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.

We investigate some dynamical effects of adding a certain amount of noise in a theoretical model for rattling in single-stage gearbox systems with a backlash, consisting of two wheels with a sinusoidal driving. The parameter intervals we are dealing with show an extremely involved attraction basin structure in phase space. One of the observable effects of noise is basin hopping, or the switching between basins of different attractors. We characterize this effect and its relation to the presence of chaotic transients.

We investigate plasma turbulence at the scrape-off layer of TCABR tokamak. We apply a power spectral analysis to the magnetic Mirnov oscillations and electrostatic fluctuations, to quantify statistical properties and to estimate the turbulence-driven radial-particle flux. A distinctive peculiarity is the modulation of electrostatic turbulence by the Mirnov oscillations shown by the partial superposition of the frequency power spectra of these two oscillations. This characteristic allows us to investigate any possible influence of the Mirnov oscillations on particle transport. In fact, a significant part of this transport occurs at the Mirnov frequencies. The effect of this modulation is also analyzed for discharges modified by external perturbations, a DC biased electrode or an ergodic magnetic limiter.

We investigate numerically the dynamical behavior of a non-ideal mechanical system consisting of a vibrating cart containing a particle which can oscillate back and forth colliding with walls carved in the cart. This system represents an impact damper for controlling high-amplitude vibrations and chaotic motion. The motion of the cart is induced by an in-board non-ideal motor driving an unbalanced rotor. We study the phase space of the cart and the bouncing particle, in particular the intertwined smooth and fractal basin boundary structure. The control of the chaotic motion of the cart due to the particle impacts is also investigated. Our numerical results suggests that impact dampers of small masses are effective to suppress chaos, but they also increase the final-state sensitivity of the system in its phase space.

The structure of magnetic field lines in a tokamak with reversed magnetic shear is investigated by means of analytically derived area-preserving non-twist Poincare maps. The basic configuration is the magnetic field produced by an ergodic limiter, superimposed to the tokamak equilibrium field in suitable coordinates. We consider the cases of one and two resonant modes, focusing on magnetic island dimerization and the formation of a transport barrier in the chaotic layer of field lines.

We investigated the structure of magnetic field lines in a tokamak with reversed magnetic shear and non-symmetric perturbations by means of analytically derived area-preserving non-twist Poincare maps. The maps are used to study magnetic island dimerization and the formation of a transport barrier in the chaotic layer of field lines.

We consider a model for rattling in single-stage gearbox systems with some backlash consisting of two wheels with a sinusoidal driving. The equations of motions are analytically integrated between two impacts of the gear teeth. Just after each impact, a mapping is used to obtain the dynamical variables. We have observed a rich dynamical behavior in such system, by varying its control parameters, and we focus on intermittent switching between laminar oscillations and chaotic bursting, as well as crises, which are sudden changes in the chaotic behavior. The corresponding transient basins in phase space are found to be riddled-like, with a highly interwoven fractal structure.

We study the scrape-off layer turbulence and transport in Tokamak Chauffage Alfven Bresilien (TCABR) before and during the launching of radio frequency excited waves that interact with the boundary plasma. We present the main characteristics of the background electrostatic fluctuations and the intermittent bursts. During the perturbation, the plasma turbulence intensity increases and the average phase velocity reverses its direction. The total turbulence driven transport and the transport radially convected by the intermittent fluctuation bursts also increase with the perturbation. The probability distributions of the bursts have long tails, resembling those typical of flight distributions with a decay parameter increasing with the wave excitation.

We study transport of passive scalar fields in a bidimensional incompressible chaotic fluid flow. For a spatially smooth velocity field with impulsive perturbations, the model is described by a randomized standard mapping. We numerically investigate passive scalar field transport for given initial concentration distributions and their dependence on the nonlinearity and noise amplitude. We show that space and time concentration histograms are determined by the underlying mechanism of stretching and folding. Moreover, to characterize this process we introduce a parameter, the average derivative of a tracer line length, which shows interesting scale properties.

We apply a model based algorithm for the calculation of the spectrum of the Lyapunov exponents of attractors of mechanical systems with impacts. For that, we introduce the transcendental maps that describe solutions of integrable differential equations, between impacts, supplemented by transition conditions at the instants of impacts. We apply this procedure to an impact oscillator and to an impact-pair system (with periodic and chaotic driving). In order to show the method precision, for large parameters range, we calculate Lyapunov exponents to classify attractors observed in bifurcation diagrams. In addition, we characterize the system dynamics by the largest Lyapunov exponent diagram in the parameter space.

We stabilize desired unstable periodic orbits, embedded in the chaotic invariant sets of mechanical systems with impacts, by applying a small and precise perturbation on an available control parameter. To obtain such perturbation numerically, we introduce a transcendental map (impact map) for the dynamical variables computed just after the impacts. To show how to implement the method, we apply it to an impact oscillator and to an impact-pair system.

Reversed magnetic shear configurations in tokamaks reduce substantially particle diffusivity and improve plasma confinement due to the formation of a transport barrier, as a result of magnetic field line reconnection and bifurcation. The latter are caused by the resonant perturbation of an ergodic limiter on a tokamak with reversed magnetic shear, which creates a region with chaotic field lines in the vicinity of the dimerized island chains. An analytically derived nontwist map for field lines is used to describe the formation of a transport barrier, manifested in the decrease of field line diffusion rate. This barrier appears due to the chaotic field line trapping near the reconnection layer that survives the bifurcation.

Basic phenomena in chaos can be associated with homoclinic and heteroclinic orbits. In this paper, we present a general numerical method to demonstrate the existence of these orbits in piecewise-linear systems. We also show that the tangency of the stable and unstable manifolds, at the onset of the chaotic double-scroll attractor, changes the basin boundaries of two α-limit sets. These changes are evidence of homoclinicity in the dynamical system. These basins give complete information about the stable manifolds around the fixed points. We show that trajectories that depart from these boundaries (for backward integration) are bounded sets. Moreover, we also show that the unstable manifolds are geometrically similar to the existing attracting sets. In fact, when no homo- (hetero-)clinic orbits exist, the attractors are ω-limit sets of initial conditions on the unstable manifolds.

We consider a symplectic map for magnetic field lines in a tokamak with an ergodic limiter, whose function is to generate a perturbing magnetic field which causes the formation of chaotic field lines in the vicinity of the tokamak inner wall. We analyze numerically the onset of global chaos due to the interaction of adjacent magnetic islands, the size of the chaotic region, and investigate anomalous diffusion and loss of field lines due to their collisions with the tokamak wall.

We consider the single mode dynamics of a self-pulsating semiconductor laser model under modulated injection current. The observation of a chaotic regime for a wide range of parameters suggests the usefulness of this model for high-speed secure optical communications. A possible way to achieve symbol encoding by using such a laser as a light source is to control its chaotic dynamics. We study the stabilization of periodic orbits embedded in the chaotic invariant set of the system by applying perturbations on the amplitude of the injection current.

Realizou-se um experimento em casa de vegetação do Departamento de Ciência do Solo da Universidade Federal de Lavras, para avaliar o efeito do silício na nutrição mineral e na produção de matéria seca de plantas de moringa submetidas ao estresse salino. Utilizaram-se o esquema fatorial e o delineamento de blocos casualizados, com três repetições, e uma planta por vaso de 3 L de capacidade, em que o primeiro fator referiu-se às doses de NaCl (0, 30, 60, 90 e 120 mol m-3) e o segundo às doses de SiO2 (0, 0,5, 1,0 e 1,5 mol m-3), em solução de Hoagland & Arnon (1950) a 50 % da concentração normal. As soluções foram renovadas em intervalos de 10 dias e, aos 35 dias, após a aplicação dos tratamentos, as plantas foram colhidas, separadas em folhas, caule e raízes, secas, para determinação da produção de matéria seca, e moídas, para determinação dos teores de N, P, K, Ca, Mg, S, Na, Cl e Si. A partir dos teores, determinaram-se as relações Na/K, Na/Ca e Na/Mg e a translocação dos nutrientes para a parte aérea. Observou-se que a adição do Si elevou os teores de K e de Ca nas folhas e reduziu os de Na e as relações Na/K, Na/Ca e Na/Mg. O Si não reduziu os efeitos depressivos do NaCl na produção de matéria seca das plantas de moringa. A greenhouse experiment was conducted in the Soil Science Department of the Federal University of Lavras, Brazil, to evaluate the effect of silicon on mineral nutrition and dry matter production of moringa plants, cultivated under salinity stress. The experiments followed a randomized factorial block-type design, in three replications. In pots of 3 L capacity with one plant each, five levels of NaCl (0, 30, 60, 90, and 120 mol m-3) were combined with four levels of SiO2 (0.0, 0.5, 1.0, and 1.5 mol m-3) in Hoagland and Arnon nutrient solution at 50 % of the normal concentration. The solutions were renewed every 10 days and the plants harvested after 45 days. Leaves, stems, and roots were separately dried for the determination of dry matter and elemental contents - N, P, K, Ca, Mg, S, Na, Cl, and Si. The relations Na/K, Na/Ca, and Na/Mg were determined. K and Ca contents increased while the Na content and the Na/K, Na/Ca, and Na/Mg relations in the leaves decreased under the influence of silicon. Silicon did not reduce the restrictive effects of NaCl on the dry matter production of the moringa plants.

The action of a set of ergodic magnetic limiters in tokamaks is investigated from the Hamiltonian chaotic scattering point of view. Special attention is paid to the influence of invariant sets, such as stable and unstable manifolds, as well as the strange saddle, on the formation of the chaotic layer at the plasma edge. The nonuniform escape process associated to chaotic field lines is also analyzed. It is shown that the ergodic layer produced by the limiters has not only a fractal structure, but it possesses the even more restrictive Wada property.

We propose a Hamiltonian formulation to study the magnetic field line structure in a tokamak with ergodic magnetic limiter. An analytical stroboscopic mapping, derived from this formulation, is used to investigate the onset of global field line chaos at the plasma edge and the Hamiltonian bifurcations of magnetic axes.

We show di2erences ofthe synchronization basins oftwo Matsumoto-Chua’s circuit (operating in either the R6 ossler-type attractor regime or the Double-Scroll-type attractor regime), coupled unidirectionally or bidirectionally through a negative feed-back controller. The knowledge of the structure ofthe synchronization basins allows one to design a communication system robust to imperfections on the setting of the initial condition. c � 2002 Elsevier Science B.V. All rights reserved.

In this work we analyze the spikes in the Ha emission, and density turbulence in runaway discharges in the TCABR tokamak. For the plasma edge density fluctuations, we find a symmetric-recurrent-type turbulence, with the same statistics found in measures of low-dimensional recurrent chaotic systems. For the plasma core fluctuations, we note that the line density oscillations are synchronized to the Ha oscillations. In addition, we suggest that both the onset of the Ha spikes and the line density oscillations are triggered by a process similar to the bifurcation responsible for the firing of neurons.

The dynamics of a negative gain suppression factor laser diode subjectedto injection current modulation is similar to that of a damped nonlinearoscillator under periodic forcing. Quasi-periodicity, frequency lockingand chaos may be present, depending on the values of the forcingparameters. We have found, for some parameter values, type-Iintermittent behavior and crisis-induced intermittency. Scaling lawswere obtained for the duration of the laminar phase and the chaos-chaosswitchings, respectively. The scale exponents are very close to thoseexpected for one-dimensional unimodal maps.

Master–slave systems have been intensively investigated for modelling the application of chaos in communications. We considered Colpitts oscillators coupled according to a master–slave configuration in order to study chaos synchronization. We revealed the existence of superpersistent transients in this coupled system. The transient is a ubiquitous phenomenon in nonlinear dynamical systems, and it is responsible for important physical phenomena. We characterized superpersistent transients through a scaling law for their average lifetime. Unstable–unstable pair bifurcation has been identified as the generic mechanism for these transients. Moreover, we showed that an additive noise, added to the slave system, may suppress the chaos synchronization. Our results show that synchronization can be achieved for higher coupling strength when there is noise. However, the noise may induce a longer transient if the synchronization is not suppressed.

In toroidally confined plasmas, the Grad-Shafranov equation, in general a non-linear PDE, describes the hydromagnetic equilibrium of the system. This equation becomes linear when the kinetic pressure is proportional to the poloidal magnetic flux and the squared poloidal current is a quadratic function of it. In this work, the eigenvalue of the associated homogeneous equation is related with the safety factor on the magnetic axis, the plasma beta and the Shafranov shift, then, the adjustable parameters of the particular solution are bounded through physical constrains. The poloidal magnetic flux becomes a linear superposition of independent solutions and its parameters are adjusted with a non-linear fitting algorithm. This method is used to find hydromagnetic equilibria with normal and reversed magnetic shear and defined values of the elongation, triangularity, aspect-ratio, and X-point(s). The resultant toroidal and poloidal beta, the safety factor at the $95\%$ flux surface and the plasma current are in agreement with usual experimental values for high beta discharges and the model can be used locally to describe reversed magnetic shear equilibria., Comment: 8 pages, 7 figures, 14 references

We analyze the electrostatic turbulence in a stationary toroidal magnetoplasma, created by radio-frequency waves and confined by a toroidal magnetic field. The increase of toroidal magnetic field leads to gradients in the mean plasma radial profiles and to the enhancement of electrostatic turbulence. Another consequence is the emergence of symmetry in the probability distributions of fluctuations and of the time in which they return to a specified reference interval of values. This symmetry as well as scaling laws reported here are typically observed in low-dimensional chaotic dynamical systems. Decreasing the magnetic field breaks the symmetry in the probability distribution; however, it preserves the correlation properties of a few average quantities.

Common statistics of turbulent electrostatic fluctuations observed at the plasma edge and scrape-off layer are analyzed in three tokamak devices that have different configurations. The statistics of experimental data collected using fixed sampling time is the same than the statistics of the time for which the oscillation return to a specified reference interval of values. This observation, in addition to the finding of power-scaling laws for some average quantities with respect to either the sampling time or the size of the reference interval, suggests that turbulence on tokamaks have recurrent characteristics, typical of a recurrent chaotic low-dimensional system. Furthermore, the first Poincare recurrence time and other dynamical tools are used to simulate the mentioned fluctuation statistical properties.

The authors numerically investigate basins of attraction of coexisting periodic and chaotic attrac tors in a gear-rattling impact model. These attractors are strongly dependent on small changes of the initial conditions. Gradually varying a control parameter, the size of these basins of attraction is modified by global bifurcations of their boundaries. Moreover, the topology of these basins is also modified by appearance or disappearance of coexisting attractors. Furthermore, for the considered control parameter range, the frac tal basin boundaries are so interleaved that trajectories are practically unpredictable in some regions of phase space. The authors also examine an example of a crisis on which a chaotic attractor is converted into a chaotic transient that goes to a periodic attractor. For this crisis, the authors show the evolution of transient lifetime dependence of the initial conditions as the control parameter is varied.