Basin of attraction of a cusp-fold singularity in 3D piecewise smooth vector fields

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

Detecting changes in the basin of attraction of a dynamical system: Application to the postural restoring system

A method that provides athree-dimensional representation ofthe basin ofattraction of a dynamical system from experimen tal data was applied tothe problem ofdynamic balance restoration. The method isbased onthe density ofthe data onthe phase space ofthe system under study and makes use ofmodeling and numerical curve fittingtools.For the dynamical system ofbalance restora tion,the shape and the size of the basin of attraction depend on the dynamics of the postural restoring mechanisms and contain important information regarding the biomechanical,as well as the neuromuscular condition of the individual. The aim ofthis work was toexamine the ability ofthe method todetect, through the observed changes inthe shape and/or the size ofthe calculated basins of attraction, (a)the inherent differences between different systems (in the current application, postural restoring systems of different individuals)and (b)induced chan ges in the same system (thepostural restoring system of an individual).The results ofthe study confirm the validity of the method and furthermore justify its robustness.

Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.

Stability region bifurcations of nonlinear autonomous dynamical systems: Type-zero saddle-node bifurcations

The behavior of stability regions of nonlinear autonomous dynamical systems subjected to parameter variation is studied in this paper. In particular, the behavior of stability regions and stability boundaries when the system undergoes a type-zero sadle-node bifurcation on the stability boundary is investigated in this paper. It is shown that the stability regions suffer drastic changes with parameter variation if type-zero saddle-node bifurcations occur on the stability boundary. A complete characterization of these changes in the neighborhood of a type-zero saddle-node bifurcation value is presented in this paper. Copyright (C) 2010 John Wiley & Sons, Ltd.

Spontaneous vegetation on overburden piles in the Coal Basin of Santa Catarina, Brazil

The objective of this work was to select indigenous vegetal species for restoration programs aiming at the regeneration of ombrophilous dense forest. Thirty-five spoil piles located in the county of Sideropolis, Santa Catarina, that received overburden disposal for 39 years (1950-1989) were selected for study because they exhibited remarkable spontaneous regrowth of trees compared to surrounding spoil piles. Floristic inventory covered the whole area of the 35 piles, whereas survey on phytosociology and natural regeneration studies were conducted in 70 plots distributed along the 35 piles. Floristic inventory recorded 83 species from 28 botanical families. Herbaceous terricolous plants constituted the predominant species (47.0%), followed by shrubs (26.5%), trees (19.3%), and vines (7.2%). Results from surveys on phytosociology and natural regeneration, focused on shrubs and trees, recorded incipient ecological succession. In addition, the most adapted species recorded on the overburden piles, as ranked by index of natural regeneration (RNT) plus importance value index (IVI), were as follows: Clethra scabra (RNT = 23.93%; IVI = 17.28%), Myrsine coriacea (RNT = 20.93%, IVI = 11.26%), Eupatorium intermedium (RNT 7.56%, IVI 0.40%), Miconia ligustroides (RNT 5.84%, IVI 2.37%), Ossaea amygdaloides (RNT 3.84%, IVI 1.30%), Tibouchina sellowiana (RNT 3.29%, M 1.94%), Eup. inulaefolium (RNT = 2.65%, IVI = 0.80%), and Baccharis dracunculifolia (RNT = 2.28%; IVI = 0.56%). High values of IVI and RNT exhibited by the exotic species Eucalyptus saligna (IVI = 21.73%, RNT = 51.41%) indicated strong competition between exotic and indigenous species. Severe chemical (acidic pH and lack of nutrients) and physical (coarse substrate and slope angle of 40-50 degrees) characteristics displayed by the overburden piles constituted limitations to floristic diversity and size of indigenous trees, indicating the need for substrate reclamation prior to forest restoration.

Stable MPC for tracking with maximal domain of attraction

In this work, a stable MPC that maximizes the domain of attraction of the closed-loop system is proposed. The proposed approach is suitable to real applications in the sense that it accounts for the case of output tracking, it is offset free if the output target is reachable and minimizes the offset if some of the constraints are active at steady state. The new approach is based on the definition of a Minkowski functional related to the input and terminal constraints of the stable infinite horizon MPC. It is also shown that the domain of attraction is defined by the system model and the constraints, and it does not depend on the controller tuning parameters. The proposed controller is illustrated with small order examples of the control literature. (C) 2011 Elsevier Ltd. All rights reserved.

Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance

This work presents an alternative way to formulate the stable Model Predictive Control (MPC) optimization problem that allows the enlargement of the domain of attraction, while preserving the controller performance. Based on the dual MPC that uses the null local controller, it proposed the inclusion of an appropriate set of slacked terminal constraints into the control problem. As a result, the domain of attraction is unlimited for the stable modes of the system, and the largest possible for the non-stable modes. Although this controller does not achieve local optimality, simulations show that the input and output performances may be comparable to the ones obtained with the dual MPC that uses the LQR as a local controller. (C) 2009 Elsevier Ltd. All rights reserved.

A strategy to fill gaps in soil survey over large spatial extents: an example from the Murray-Darling basin of Australia

We re-mapped the soils of the Murray-Darling Basin (MDB) in 1995-1998 with a minimum of new fieldwork, making the most out of existing data. We collated existing digital soil maps and used inductive spatial modelling to predict soil types from those maps combined with environmental predictor variables. Lithology, Landsat Multi Spectral Scanner (Landsat MSS), the 9-s digital elevation model (DEM) of Australia and derived terrain attributes, all gridded to 250-m pixels, were the predictor variables. Because the basin-wide datasets were very large data mining software was used for modelling. Rule induction by data mining was also used to define the spatial domain of extrapolation for the extension of soil-landscape models from existing soil maps. Procedures to estimate the uncertainty associated with the predictions and quality of information for the new soil-landforms map of the MDB are described. (C) 2002 Elsevier Science B.V. All rights reserved.

Contrasts in the basins of attraction of structurally identical iterative root finding methods

A numerical comparison is performed between three methods of third order with the same structure, namely BSC, Halley’s and Euler–Chebyshev’s methods. As the behavior of an iterative method applied to a nonlinear equation can be highly sensitive to the starting points, the numerical comparison is carried out, allowing for complex starting points and for complex roots, on the basins of attraction in the complex plane. Several examples of algebraic and transcendental equations are presented.

Adaptive tackling of the swinging problem for a 2 DOF crane – payload system

The control of a crane carrying its payload by an elastic string corresponds to a task in which precise, indirect control of a subsystem dynamically coupled to a directly controllable subsystem is needed. This task is interesting since the coupled degree of freedom has little damping and it is apt to keep swinging accordingly. The traditional approaches apply the input shaping technology to assist the human operator responsible for the manipulation task. In the present paper a novel adaptive approach applying fixed point transformations based iterations having local basin of attraction is proposed to simultaneously tackle the problems originating from the imprecise dynamic model available for the system to be controlled and the swinging problem, too. The most important phenomenological properties of this approach are also discussed. The control considers the 4th time-derivative of the trajectory of the payload. The operation of the proposed control is illustrated via simulation results.

An Extension of Estimation of Domain of Attraction for Fractional Order Linear System Subject to Saturation Control

This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

Efficacy of sulfadoxine-pyrimethamine and mefloquine for the treatment of uncomplicated Plasmodium falciparum malaria in the Amazon basin of Peru

In vivo antimalarial drug efficacy studies of uncomplicated Plasmodium falciparum malaria at an isolated site in the Amazon basin of Peru bordering Brazil and Colombia showed >50% RII/RIII resistance to sulfadoxine-pyrimethamine but no evidence of resistance to mefloquine.

A new sand fly in the subgenus Nyssomyia (Diptera, psychodidae) from the Amazon basin of Brazil

Lutzomyia (Nyssomyia) waltoni m.sp., uma nova espécie de flebótomo é descrita e ilustrada. Observações ecológicas disponíveis são apresentadas. (AU)

A Model-to-model analysis of the repeated Prisoners' Dilemma: genetic algorithms vs. evolutionary dynamics

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the analytical model. Our main conclusion is that analytical and computational models are good complements for research in social sciences. Indeed, while on the one hand computational models are extremely useful to extend the scope of the analysis to complex scenar

Effects of immigration on the prevalence of malaria in rural areas of the Amazon basin of Brazil

Epidemiological studies were conducted on malaria in three rural areas of the Amazon basin in the State of Rondônia: the town of Costa Marques, Forte Príncipe da Beira (Fort), and an immigrant settlement in the nearby forest. These studies were instituted to document the malaria problem and to describe the role of immigration on its distribution and prevalence. Hospital records in the town show that the number of malaria cases increased five fold from 1983 to 1987 and that the predominant malaria parasite changel from Plasmodium vivax to P. falciparum. Increased malaria followed increased immigration and colonization of the forest. A series of epidemiologic studies suggested the linkage between malaria and immigration as the prevalence of malaria was 1-2% at the Fort, a stable community, 8-9% at Costa Marques, a growing community, and 14-26% in the new settlements in the forest.