Table of contents

This proceedings presents selected contributions from the participants of South America Dynamics Days 2011, which was hosted by the National Institute for Space Research (INPE), Brazil, in July 2010.

Dynamics Days was founded in 1980 and is the longest standing and most respected international series of meetings devoted to the field of dynamics and nonlinearity. Traditionally it has brought together researchers from a wide range of backgrounds – including physics, biology, engineering, chemistry and mathematics – for interdisciplinary research into nonlinear science.

Dynamics Days South America 2010 marked the beginning of the South American branch of Dynamics Days. It brought together, for the first time in South America, researchers from a wide range of backgrounds who share a common interest in the theory and applications of nonlinear dynamics. Thus, South American researchers had a forum to promote regional as well as international scientific and technological exchange and collaboration especially, but not exclusively, on problems that are particularly relevant for the development of science and technology in the South American region. Furthermore, the conference also brought together prominent scientists from around the world to review recent developments in nonlinear science.

This conference comprised plenary invited talks, minisymposia, contributed talks and poster sessions. The articles that are compiled here were chosen from among the works that were presented as contributed talks and posters. They represent a good selection which allows one to put issues that were discussed during the conference into perspective.

It is possible to evaluate the success of an initiative by using several indices. In relation to attendees, the conference had 311 participants from 22 countries, who presented 341 works. About 86% of the participants came from South American countries. These figures allow one to classify this Dynamics Days conference as that with the greatest number of attendees ever.

Finally, we would like to express our gratitude to all the participants for their presentations, discussions, and remarkable interactions with one another. The tireless work undertaken by all the members of the International Advisory Committee and the Organizing Committee must also be recognized. We also wish to express our deep appreciation for the Scientific Societies and Research Support Agencies which supported the conference and provided all the resources which were necessary to make this idea of a South American Dynamics Days come true.

Elbert E N Macau, Tiago Pereira, Antonio F B A Prado, Luiz F R Turci, and Othon C WinterEditors

International Advisory Committee

Adilson E Motter Northwestern University Evanston – IL – USA

Alfredo Ozorio Centro Brasileiro de Pesquisas Físicas Rio de Janeiro – RJ – Brazil

Celso Grebogi (Chair) University of Aberdeen Aberdeen – UK

Ed Ott University of Maryland College Park – MD – USA

Epaminondas Rosa Jr Illinois State University Normal – IL – USA

Hans Ingo Weber Pontifícia Universidade Católica Rio de Janeiro – RJ – Brazil

Holger Kantz Max Planck Institute for the Physics of Complex Systems Dresden – Germany

Jason Gallas (Co-chair) Universidade Federal do Rio Grande do Sul Porto Alegre – RS – Brazil

José Roberto Rios Leite Univ. Federal de Pernanbuco Recife – PE – Brazil

Jürgen Kurths Potsdam Institute for climate Impact Research Humboldt University, Berlin – Germany

Kenneth Showalter West Virginia University Morgantown – WV – USA

Lou Pecora Naval Research Lab Washington – DC – USA

Luis Antonio Aguirre Universidade Federal de Minas Gerais Belo Horizonte – MG – Brazil

Marcelo Viana IMPA – Instituto Nacional de Matemática Pura e Aplicada Rio de Janeiro – RJ – Brazil

Miguel A F Sanjuán Universidad Rey Juan Carlos Madrid – Spain

Paulo Roberto de Souza Mendes Pontifícia Universidade Católica Rio de Janeiro – RJ – Brazil

Roland Korbele Universidade de São Paulo São Carlos – SP – Brazil

Rubens Sampaio Pontifícia Universidade Católica Rio de Janeiro – RJ – Brazil

Ruedi Stoop Swiss Federal Institute of Technology UZH/ETHZ Zurich – Switzerland

Sylvio Ferraz Mello Universidade de São Paulo São Paulo – SP – Brazil

Takashi Yoneyama ITA – Instituto Tecnológico de Aeronáutica São José dos Campos – SP – Brazil

Ying-Cheng Lai Arizona State University Tempe – AZ – USA

Organizing Committee

Antonio Carlos Roque da Silva USP – Universidade de São Paulo Ribeirão Preto – SP – Brazil

Antonio F Bertachini de Almeida Prado (Co-chair) INPE – Instituto Nacional de Pesquisas Espaciais São José dos Campos – SP – Brazil

Arturo C Marti Facultad de Ciencia Montevideo – Uruguai

Carlos Leopoldo Pando Lambruschini Benemérita Universidad Autónoma de Puebla Puebla – Mexico

Edson Denis Leonel UNESP – "Júlio de Mesquisa Filho" Rio Claro – SP – Brazil

Elbert E N Macau (Chair) INPE – Instituto Nacional de Pesquisas Espaciais São José dos Campos – SP – Brazil

Gerard Olivar Tost Universidad National de Colombia Manizales – Colombia

Hamilton Varela USP – Universidade de São Paulo São Carlos – SP – Brazil

Hilda Cerdeira (Co-chair) IFT – Instituto de Física Teórica São Paulo – SP – Brazil

Iberê Luiz Caldas USP – Universidade de São Paulo São Paulo – SP – Brazil

José Manoel Balthazar UNESP – "Júlio de Mesquisa Filho" Rio Claro – SP – Brazil

José Roberto Castilho Piqueira USP – Universidade de São Paulo São Paulo – SP – Brazil

Luciano da Fontoura Costa USP – Universidade de São Paulo São Carlos – SP – Brazil

Luiz de Siqueira Martins Filho UFABC – Universidade Federal do ABC Santo André – SP – Brazil

Marcel G Clerc Universidad de Chile Santiago – Chile

Miguel Vizcardo Universidad de Arequipa Arequipa – Peru

Gonzalo Marcelo Ramirez Ávila Universidad Mayor de San Andrés La Paz – Bolivia

Marco Aurélio Pires Idiart Universidade Federal do Rio Grande do Sul Porto Alegre – RS – Brazil

Marcus de Aguiar UNICAMP Campinas – SP – Brazil

Mario Cosenza Universidad de Los Andes Merida – Venezuela

Othon Cabo Winter UNESP – "Júlio de Mesquisa Filho" Guaratinguetá – SP – Brazil

Ricardo Luiz Viana Universidade Federal do Paraná Curitiba – PA – Brazil

Silvina Ponce Dawson Universidad de Buenos Aires Buenos Aires – Argentina

Vivian M Gomes INPE – Instituto Nacional de Pesquisas Espaciais São José dos Campos – SP – Brazil

Realization

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All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

In this work we consider a situation in which the two parameters of a Hénon map are linearly modulated by the output of another Hénon map, whose parameters are constant in time but can be adjusted. More specifically, here we numerically investigate modifications in basins of attraction of coexisting states, and shift in the location of critical points in bifurcation diagrams of a Hénon map, by virtue of periodic parametric modulation from another Hénon map.

We present a simple method to analyze time series, and estimate the parameters needed to control chaos in dynamical systems. Application of the method to a system described by the logistic map is also shown. Analyzing only two 100-point time series, we achieved results within 2% of the analytical ones. With these estimates, we show that OGY control method successfully stabilized a period-1 unstable periodic orbit embedded in the chaotic attractor.

Electrochemistry is a prone field for observing complex behavior such as simple and mixed-mode oscillations, chaos and spatiotemporal pattern formation. Although modeling and numerical analysis of those systems is relatively common, analysis of the inner structure of the oscillatory region is a rather unexplored issue. We describe in this paper a numerical study of a surface catalyzed reaction that is being poisoned by a foreign adsorbing species. The effect of the poison coverage on the oscillatory period and amplitude is discussed with the help of parameter plane diagrams and mechanistic analysis. A coherent picture explaining the effect of the poison adsorption on the dynamic features is then constructed based on the obtained data.

In this work we present evidence of the self-organized criticality behavior of the plasma edge electrostatic turbulence in the tokamak TCABR. Analyzing fluctuation data measured by Langmuir probes, we verify the radial dependence of self-organized criticality behavior at the plasma edge and scrape-off layer. We identify evidence of this radial criticality in statistical properties of the laminar period distribution function, power spectral density, autocorrelation, and Hurst parameter for the analyzed fluctuations.

We report a numerical bifurcation study on the Chua's circuit with parallel resistor. Through the largest Lyapunov exponent, we constructed a two-dimensional parameter space of the model. We also implemented the experimental circuit to show the similarities between the model and the experimental data. With that modification we discuss the effect of a parallel resistor in the dynamics of a Chua's circuit.

Liquid foams have fascinating optical properties, which are caused by the large number of light refractions and reflections by liquid films and Plateau borders. Due to refraction and reflection at the interfaces, the direction of the rays leaving a Plateau border can vary greatly for the same incident angle and a small positional offset. A close look in some configurations of the Plateau borders or liquid bridges reveals the existence of some triangular patterns surrounded by a complex structure, and these patterns bear a resemblance to those observed in some systems involving chaotic scattering and multiple light reflections between spheres. Provided the optical properties of the sphere surfaces are chosen appropriately, fractals are natural consequences of multiple scattering of light rays in these cavities. The cavity acts as a hyperbolic kaleidoscope multiplying the scattering of light rays generating patterns related to Poincaré disks and Sierpinski gaskets in comparison to linear kaleidoscopes. We present some experimental results and simulations of these patterns explained by the light of the chaotic scattering.

Many stochastic time series can be described by a Langevin equation composed of a deterministic and a stochastic dynamical part. Such a stochastic process can be reconstructed by means of a recently introduced nonparametric method, thus increasing the predictability, i.e. knowledge of the macroscopic drift and the microscopic diffusion functions. If the measurement of a stochastic process is affected by additional strong measurement noise, the reconstruction process cannot be applied. Here, we present a method for the reconstruction of stochastic processes in the presence of strong measurement noise, based on a suitably parametrized ansatz. At the core of the process is the minimization of the functional distance between terms containing the conditional moments taken from measurement data, and the corresponding ansatz functions. It is shown that a minimization of the distance by means of a simulated annealing procedure yields better results than a previously used Levenberg-Marquardt algorithm, which permits a rapid and reliable reconstruction of the stochastic process.

Stabilization of a chaotic system in one of its unstable equilibrium points by applying small perturbations is studied. A two-stage control strategy based on linear feedback control is applied. Improvement of system performance is addressed by exploiting the ergodicity of the original dynamics and using Lyapunov stability results for control design. Extension to the not complete observability case is also analyzed.

Bipartite networks and the nestedness concept appear in two different contexts in theoretical ecology: community ecology and islands biogeography. From a mathematical perspective nestedness is a pattern in a bipartite network. There are several nestedness indices in the market, we used the index ν. The index ν is found using the relation ν = 1 − τ where τ is the temperature of the adjacency matrix of the bipartite network. By its turn τ is defined with help of the Manhattan distance of the occupied elements of the adjacency matrix of the bipartite network. We prove that the nestedness index ν is a function of the connectivities of the bipartite network. In addition we find a concise way to find ν which avoid cumbersome algorithm manupulation of the adjacency matrix.

In this work we analyze the particle transport at the plasma edge during TCABR tokamak discharges with high MHD activity. The interpretation of this transport as chaotic, in a quasi integrable Hamiltonian system formed by the plasma flow and the drift waves, predicts its dependence on a confinement parameter, proportional to the difference between the plasma flow and the drift wave phase velocities. For the analyzed discharges, we observe a particle transport decrease where the confinement parameter has a maximum. In the considered quasi integrable description, this can be interpreted as an evidence of a localized transport barrier.

A non-twist Hamiltonian system perturbed by two waves with particular wave numbers can present Robust Tori, barriers created by the vanishing of the perturbing Hamiltonian at some defined positions. When Robust Tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. We analyze the breaking up of the RT as well the transport dependence on the wave numbers and on the wave amplitudes. Moreover, we report the chaotic web formation in the phase space and how this pattern influences the transport.

In the present work, we determine the fraction of magnetic field lines that reach the tokamak wall leaving the plasma surrounded by a chaotic layer created by resonant perturbations at the plasma edge. The chaotic layer arises in a scenario where an integrable magnetic field with reversed magnetic shear is perturbed by an ergodic magnetic limiter. For each considered line, we calculate its connection length, i.e. the number of toroidal turns that the field lines complete before reaching the wall. We represent the results in the poloidal section in which the initial coordinates are chosen. We also estimate the radial profile of the fraction of field lines, for different temperatures, whose connection lengths are smaller than the electron collisional mean free path.

This work presents an electrical implementation of complete synchronization systems, proposing a master/slave synchronization of two identical particle-in-a-box electronic circuits, exhibiting a rich chaotic behaviour. This behaviour was measured, and also emulated, and the results were compared. Just a few works in literature describe experimental measurements of chaotic systems. The master/slave electronic circuits employed have a very simple electronic implementation and results show a complete synchronization of the system.

Conventional approaches to modeling any system try to incorporate increasingly realistic features into the model, thereby making it more and more complex. An opposite approach seeks to build simpler and simpler conceptual models capable of capturing some observed features of a system. This trend began with Lorenz, who simplified models of the atmosphere to obtain the Lorenz model consisting of a system of only three equations. Despite the simplicity of these equations, this system displayed surprisingly rich properties, and has been used as a conceptual model in diverse disciplines. Poincare maps help study ordinary differential equations from a qualitative perspective. Several investigators like Henon and Feigenbaum followed this simplification approach. Instead of investigating Poincare maps of realistic systems, they, along with several others, investigated simple maps for their own sake. Despite lack of realism, this approach proved to be very fruitful. A map, as simple as the Logistic map, became an important conceptual modeling paradigm. It provided a tool for understanding bifurcation routes to chaos, which were verified experimentally through various experiments in diverse fields. Coupled map lattices (CML) help explore partial differential equations (PDE). Further simplification led to the introduction of Cellular Automata (CA). These fields continue to be explored with vigor and have given rise to a rich body of knowledge, conceptually useful over a wide spectrum of disciplines. In this paper, we follow the simplification approach for modeling the N-body problem. N-body simulations, say in Gravitation, give rise to filamentary structures. Such structures are observed in the actual observed Galactic distribution. The mechanism for creation of such structures is not well understood. We present a simple iterative dynamical model, motivated by the N-body problem, which, though unrealistic, produces such filamentary structures. This model also exhibits a variety of intriguing structures. Attempts to understand these structures may lead to useful insights similar to those provided by investigations in maps, CML, CA etc.

In this work we considered cellular automaton model with time delay. Time delay included in this model reflects the delay between the time in which the site is affected and the time in which its variable is updated. We analyzed the effect of the rules on the dynamics through the cluster counting. According to this cluster counting, the dynamics behavior is investigated. We verified periodic oscillations same as delay differential equation. We also studied the relation between the time delay in the cell cycle and the time to start the metastasis, using suitable numerical diagnostics.

in this paper, we study the existence of a solution for a fourth order boundary value problem Where f ∊ C([0,l]× IR², IR), and f ∊ C([0,l]× IR³, IR). By placing certain restrictions on the nonlinear term f, we prove the existence of at least one solution to the boundary-value problem with the use of lower and upper solution method and Schauder fixed-point theorem. The construction of lower or upper solutions is also presented.

In this paper we report a new four-dimensional autonomous system, constructed from a Lorenz system by introducing an adequate feedback controller to the third equation. We use a numerical method that considers the second largest Lyapunov exponent value as a measure of hyperchaotic motion, to construct a two-dimensional parameter-space color plot for this system. Different levels of hyperchaos are represented in this plot by a continuously changing yellow-red scale. Practical applications of this plot includes, by instance, walking in the parameter-space of hyperchaotic systems along suitable paths.

A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behaviour observed in the incidence of real infectious diseases, such as oscillations and irregularities. For this purpose we introduce, in a naïve discrete-time SIRS model, seasonal variability in the loss of immunity and in the infection probability, modelled by sequences of kicks. Restrictive assumptions are made on the parameters of the models, in order to guarantee that the transitions are determined by true probabilities, so that comparisons with stochastic discrete-time previsions can be also provided. Numerical simulations show that the characteristics of real infectious diseases can be adequately modeled.

In the last years, chaotic systems have been applied in information security. These systems have a complex and unpredictable behavior, what makes them more attractive for data cryptography applications. In this work, the chaotic behavior of signals generated by Chua's system is combined with the original information in order to obtain a safe cryptographic method. The experimental results demonstrate that the proposed scheme can be used in data cryptography applications.

In the present work we use an asymptotic approach to obtain the long wave equations. The shallow water equation is put as a function of an external parameter that is a measure of both the spatial scales anisotropy and the fast to slow time ratio. The values given to the external parameters are consistent with those computed using typical values of the perturbations in tropical dynamics. Asymptotically, the model converge toward the long wave model. Thus, it is possible to go toward the long wave approximation through intermediate realizable states. With this approach, the resonant nonlinear wave interactions are studied. To simplify, the reduced dynamics of a single resonant triad is used for some selected equatorial trios. It was verified by both theoretical and numerical results that the nonlinear energy exchange period increases smoothly as we move toward the long wave approach. The magnitude of the energy exchanges is also modified, but in this case depends on the particular triad used and also on the initial energy partition among the triad components. Some implications of the results for the tropical dynamics are disccussed. In particular, we discuss the implications of the results for El Niño and the Madden-Julian in connection with other scales of time and spatial variability.

In this paper we examine a Cournot duopoly model, which expresses the strategic interaction between two firms. We formulate the dynamic adjustment process and investigate the dynamic properties of the stationary point. By introducing a memory mechanism characterized by distributed lag functions, we presuppose that each firm makes production decisions in a cautious manner. This implies that we have to deal with the system of integro-differential equations. By means of numerical simulations we show the occurrence of chaotic fluctuations in the case of fixed delays.

The Sznajd model is a sociophysics model that is based in the Potts model, and used for describing opinion propagation in a society. It employs an agent-based approach and interaction rules favouring pairs of agreeing agents. It has been successfully employed in modeling some properties and scale features of both proportional and majority elections (see for instance the works of A. T. Bernardes and R. N. Costa Filho), but its stationary states are always consensus states. In order to explain more complicated behaviours, we have modified the bounded confidence idea (introduced before in other opinion models, like the Deffuant model), with the introduction of prejudices and biases (we called this modification confidence rules), and have adapted it to the discrete Sznajd model. This generalized Sznajd model is able to reproduce almost all of the previous versions of the Sznajd model, by using appropriate choices of parameters. We solved the attractor structure of the resulting model in a mean-field approach and made Monte Carlo simulations in a Barabási-Albert network. These simulations show great similarities with the mean-field, for the tested cases of 3 and 4 opinions. The dynamical systems approach that we devised allows for a deeper understanding of the potential of the Sznajd model as an opinion propagation model and can be easily extended to other models, like the voter model. Our modification of the bounded confidence rule can also be readily applied to other opinion propagation models.

We introduce a new method to improve Markov maps by means of a Bayesian approach. The method starts from an initial map model, wherefrom a likelihood function is defined which is regulated by a temperature-like parameter. Then, the new constraints are added by the use of Bayes rule in the prior distribution. We applied the method to the logistic map of population growth of a single species. We show that the population size is limited for all ranges of parameters, allowing thus to overcome difficulties in interpretation of the concept of carrying capacity known as the Levins paradox.

We studied the dynamical evolution of asteroids in terrestrial planet crossing orbits, located between 2.1 and 2.5 AU. The evolution is analyzed by direct numerical integration of massless particles under the gravitational influence of all planets from Venus to Neptune. The simulations include the Yarkovsky effect, introduced as a non conservative force that produces a slow variation of the average orbital semimajor axis. Our analysis focuses on the test particles that can reach the middle and outer regions of the Main Belt (semimajor axis > 2.5 AU) during their evolution, since these may be relevant for understanding the transport mechanisms of asteroids from the inner Belt. These mechanisms could help to explain, for example, the existence of basaltic asteroids beyond 2.5 AU assuming that these bodies originate in the Vesta family, located at ∼ 2.3 AU. We found that, although some orbits that reach the middle and outer regions of the Belt can become temporarily detached from the planet crossing regime, and may have their orbital eccentricities damped due to capture at some mean motion resonances, such orbits survive for only a few hundred thousand years and, ultimately, the test particles return to the planet crossing regime being eventually discarded by close encounters with the planets. These results seem to indicate that a transport mechanism based only on planetary encounters and resonant capture might not be efficient enough to justify the presence of basaltic asteroids beyond 2.5 AU.

The task of navigating to a target position in space is a fairly common task for a mobile robot. It is desirable that this task is performed even in previously unknown environments. One reactive architecture explored before addresses this challenge by denning a hand-coded coordination of primitive behaviours, encoded by the Potential Fields method. Our first approach to improve the performance of this architecture adds a learning step to autonomously find the best way to coordinate primitive behaviours with respect to an arbitrary performance criterion. Because of the limitations presented by the Potential Fields method, especially in relation to non-convex obstacles, we are investigating the use of Relational Reinforcement Learning as a method to not only learn to act in the current environment, but also to generalise prior knowledge to the current environment in order to achieve the goal more quickly in a non-convex structured environment. We show the results of our previous efforts in reaching goal positions along with our current research on generalised approaches.

Fireflies constitute a paradigm of pulse-coupled oscillators. In order to tackle the problems related to synchronisation transients of pulse-coupled oscillators, a Light-Controlled Oscillator (LCO) model is presented. A single LCO constitutes a one-dimensional relaxation oscillator described by two distinct time-scales meant to mimic fireflies in the sense that: it is capable of emitting light in a pulse-like fashion and detect the emitted by others in order to adjust its oscillation. We present dynamical results for two interacting LCOs in the torus for all possible coupling configurations. Transient times to the synchronous limit cycle are obtained experimentally and numerically as a function of initial conditions and coupling strengths. Scaling laws are found based on dimensional analysis and critical exponents calculated, thus, global dynamic is restricted. Furthermore, an analytical orthogonal transformation that allows to calculate Floquet multipliers directly from the time series is presented. As a consequence, local dynamics is also fully characterized. This transformation can be easily extended to a system with an arbitrary number of interacting LCOs.

In this work the discretization of the Hénon-Heiles system obtained by applying the Monaco and Normand-Cyrot method is investigated. In order to obtain dynamically valid models, several approaches covering from the choice of terms in the difference equation originated from the discretization process to the increase of the discretization order are analyzed. As a conclusion it is shown that discretized models that preserve both the symmetry and the stability of their continuous counterpart can be obtained, even for large discretization steps.

Analytical expressions for the invariant densities for a class of discrete two dimensional chaotic systems are given. The method of separation of variables for the associated Frobenius-Perron equation is introduced. These systems are related to nonlinear difference equations which are of the type x_k+2 = T(x_k). The function T is a chaotic map of an interval whose chaotic behaviour is inherited to the two dimensional one. We work out in detail some examples, with T an expansive or intermittent map, in order to expose the method. Finally, we discuss how to generalize the method to higher dimensional maps.

In this work we focus on interaction networks between insects and plants and in the characterization of insect plant asymmetry, an important issue in coevolution and evolutionary biology. We analyze in particular the asymmetry in the interaction matrix of animals (herbivorous insects) and plants (food resource for the insects). Instead of driving our attention to the interaction matrix itself we derive two networks associated to the bipartite network: the animal network, D₁, and the plant network, D₂. These networks are constructed according to the following recipe: two animal species are linked once if they interact with the same plant. In a similar way, in the plant network, two plants are linked if they interact with the same animal. To explore the asymmetry between D₂ and D₁ we test for a set of 23 networks from the ecologic literature networks: the difference in size, ΔL, clustering coefficient difference, ΔC, and mean connectivity difference, Δ<k>. We used a nonparametric statistical test to check the differences in ΔL, ΔC and Δ<k>. Our results indicate that ΔL and Δ<k> show a significative asymmetry.

This work studies the dynamical behavior of breathers in a single nonlinear lattice under the influence of energy changes. To create the breather we used the anti-continuous limit and studied its stability through the Floquet theory. Using the information entropy we calculated the effective number of oscillators with significant energy and determined if there is or not the formation of a spatially localized structure.

In literature the phenomenon of diffusion has been widely studied, however for nonextensive systems which are governed by a nonlinear stochastic dynamic, there are a few soluble models. The purpose of this study is to present the solution of the nonlinear Fokker-Planck equation for a model of potential with barrier considering a term of absorption. Systems of this nature can be observed in various chemical or biological processes and their solution enriches the studies of existing nonextensive systems.

This paper presents a method for the quantification of cellular rejection in endomyocardial biopsies of patients submitted to heart transplant. The model is based on automatic multilevel thresholding, which employs histogram quantification techniques, histogram slope percentage analysis and the calculation of maximum entropy. The structures were quantified with the aid of the multi-scale fractal dimension and lacunarity for the identification of behavior patterns in myocardial cellular rejection in order to determine the most adequate treatment for each case.

We present a spatial array of Lorenz oscillators, with each cell lattice in the chaotic regime. This system shows spatial ordering due to self-organization of chaos synchronization after a bifurcation. It is shown that an array of such oscillators transformed under a discrete symmetry group, does not maintain the global dynamics, although each transformed unit cell is locally identical to its precursor. Alternatively, it is shown that in a 1-dimensional lattice, the coupling destroy the chaotic behavior but there are similar global behaviors between both coupled arrays, suggesting that is the local equivariance which controls the dynamics.

The correct modeling for processes involving convection, without introducing excessive artificial damping while retaining high accuracy, stability, boundedness and simplicity of implementation continues being nowadays a challenging task for CFD practitioners. The objective of this study is to present and evaluate the performance of two new upwinding schemes, namely SDPUS-C1 and EPUS, for nonlinear convection term discretization. Both SDPUS-C1 and EPUS schemes satisfy the TVD principle of Harten and are based on the NVD formulation of Leonard. Firstly, a description of the schemes is presented and then the numerical results are provided for one- and two-dimensional hyperbolic conservation laws. Finally, as an application, the SDPUS-C1 and EPUS schemes are employed for the simulation of two-dimensional incompressible fluid flows involving moving free surfaces. The numerical experiments show that the proposed upwinding schemes perform very well.

Topological analysis of chaotic dynamical systems emerged in the nineties as a powerful tool in the study of strange attractors in low-dimensional dynamical systems. It is based on identifying the stretching and squeezing mechanisms responsible for creating a strange attractor and organize all the unstable periodic orbits in this attractor. This method is concerned with the manifold generated by the chaotic system. Furthermore, as a mathematical object, the manifolds have a well studied geometric and algebraic structure, particularly for the case of compact surfaces. Intending to use this structure in the analysis and application of chaotic systems through their topological characteristics, we determine properties of geodesic codes for compact surfaces necessary for the construction of encoders from the symbolic sequences of experimental data generated by the unstable periodic orbits of the strange attractor (related to the behavior changes of the system with the variation of control parameters) to the geodesic code sequences, which permits to use the surface structure to study the system orbits.

Description of a physical phenomenon through differential equations has errors involved, since the mathematical model is always an approximation of reality. For an operational prediction system, one strategy to improve the prediction is to add some information from the real dynamics into mathematical model. This aditional information consists of observations on the phenomenon. However, the observational data insertion should be done carefully, for avoiding a worse performance of the prediction. Technical data assimilation are tools to combine data from physical-mathematics model with observational data to obtain a better forecast. The goal of this work is to present the performance of the Neural Network Multilayer Perceptrons trained to emulate a Variational method in context of data assimilation. Techniques for data assimilation are applied for the Lorenz systems; which presents a strong nonlinearity and chaotic nature.

It is shown that nonlocal interactions and phenomena can be achieved through local considerations, in which the departure of some scalar field from an harmonic one in a point changes as a function of the field itself in such point. After discretizing the equation of motion, it is shown that the shape of the nonlocal interaction function depends deeply on the choice of boundary conditions. As a physical implementation, the found interactions describes the evolution for the inductively coupled nonlinear networks. A qualitative analysis suggests that under such interactions the system self-organizes quite naturally, finally this is evidenced through the numerical solution of the equations of motion in the case of local cubic nonlinearities for two different boundary conditions.

A stochastic cellular automata model for wildland fire spread under flat terrain and no-wind conditions is proposed and its dynamics is characterized and analyzed. One of three possible states characterizes each cell: vegetation cell, burning cell and burnt cell. The dynamics of fire spread is modeled as a stochastic event with an effective fire spread probability S which is a function of three probabilities that characterize: the proportion of vegetation cells across the lattice, the probability of a burning cell becomes burnt, and the probability of the fire spread from a burning cell to a neighboring vegetation cell. A set of simulation experiments is performed to analyze the effects of different values of the three probabilities in the fire pattern. Monte-Carlo simulations indicate that there is a critical line in the model parameter space that separates the set of parameters which a fire can propagate from those for which it cannot propagate. Finally, the relevance of the model is discussed under the light of computational experiments that illustrate the capability of the model catches both the dynamical and static qualitative properties of fire propagation.

Although undesired in many applications, the intrinsic and spurious spatial inhomogeneity that permeates real systems is the forerunner instability that leads high-intensity charged particle beams to its equilibrium. In general, this equilibrium is reached in a particular way, by the development of a tenuous particle population around the original beam, conventionally known as the halo. In this direction, the purpose of this work is to analyze the influence of the magnitude of the initial inhomogeneity over the dynamics of quasi-homogeneous mismatched beams. For that, all beam constituent particles, which are initially disposed in an equidistant form, suffer a progressive perturbation through a noise of a variable amplitude. Beam quantities are quantified as functions of the noise amplitude, which indirectly is assumed a consistent measure of the initial beam inhomogeneity. The results have been obtained by the means of full self-consistent N-particle beam numerical simulations and seem to be an important complement to the investigations already carried out in prior works.

We present a minimalist model to describe the interplay between burst firing and calcium dynamics in Gonadotropin-releasing hormone (GnRH) cells. This model attempts to give a qualitative representation of Duan's model [3], and it comprises two FithzHugh-Nagumo (FHN) coupled systems describing the dynamics of the membrane potential and calcium concentration in the GnRH cells. Within the framework of our minimalist model, we find that the calcium subsystem drives burst firing by making the voltage subsystem to undergo a Hopf bifurcation. Specifically, fast relaxation oscillations occur in a specific region of the c–z plane (c being the calcium concentration, and z a calcium-dependent gating variable). Slow calcium oscillations, instead, are carried by the voltage subsystem by successive shifts of the calcium steady state, and have the net effect of an external perturbation. The full comprehension of the phase-plane of the voltage subsystem and the 3-dimensional phase-space of the calcium subsystem ultimately allows us to study the behaviours of the entire model under the change of certain parameters. Those special parameters do not necessarily follow realistic assumptions, but merely intend to mimic some pharmacological tests which have been performed experimentally and also simulated by Duan's model under the corresponding physiological considerations.

In this article we report a theoretical model based on Green's functions and averaging techniques that describes the dynamics of parametrically-driven mechanical resonators under the action of thermal noise. Quantitative estimates for quadrature thermal noise squeezing near the first parametric instability zone of the oscillator are given. Furthermore, the parameter space where these phenomena occur is presented. Very good agreement between analytical estimates and numerical results is achieved.

We investigate a generalisation of the logistic map as x_n+1 = 1 − ax_n ⊗_qmapx_n (−1 ≤ x_n ≤ 1, 0 < a ≤ 2) where ⊗q stands for a generalisation of the ordinary product, known as q-product [Borges, E.P. Physica A 340, 95 (2004)]. The usual product, and consequently the usual logistic map, is recovered in the limit q → 1, The tent map is also a particular case for q_map → ∞. The generalisation of this (and others) algebraic operator has been widely used within nonextensive statistical mechanics context (see C. Tsallis, Introduction to Nonextensive Statistical Mechanics, Springer, NY, 2009). We focus the analysis for q_map > 1 at the edge of chaos, particularly at the first critical point a_c, that depends on the value of q_map. Bifurcation diagrams, sensitivity to initial conditions, fractal dimension and rate of entropy growth are evaluated at a_c(q_map), and connections with nonextensive statistical mechanics are explored.

In this work we address the statistical periodicity phenomenon on a coupled map lattice. The study was done based on the asymptotic binary patterns. The pattern multiplicity gives us the lattice information capacity, while the entropy rate allows us to calculate the locking-time. Our results suggest that the lattice has low locking-time and high capacity information when the coupling is weak. This is the condition for the system to reproduce a kind of behavior observed in neural networks.

We present a simple model for neural signaling leaps in the brain considering only the thermodynamic (Nernst) potential in neuron cells and brain temperature. We numerically simulated connections between arbitrarily localized neurons and analyzed the frequency distribution of the distances reached. We observed qualitative change between Normal statistics (with T = 37.5°C, awaken regime) and Lévy statistics (T = 35.5°C, sleeping period), characterized by rare events of long range connections.

In this work, we investigated the mesoscale dynamics of the Brazil-Malvinas Confluence (BMC) region. Particularly, we were interested in the role of geophysical instability in the formation and development of the mesoscale features commonly observed in this region.

We dynamically analyzed the results of numerical simulations of the BMC region conducted with 'Hybrid Coordinate Ocean Model' (HYCOM). We quantified the effect of barotropic and baroclinic energy conversions in the modeled flow and showed the dominance of the latter in the region.

This work propose a detection and alert algorithm for muscle fatigue in paraplegic patients undergoing electro-therapy sessions. The procedure is based on a mathematical chaotic model emulating physiological signals and Continuous Wavelet Transform (CWT). The chaotic model developed is based on a logistic map that provides suitable data accomplishing some physiological signal class patterns. The CWT was applied to signals generated by the model and the resulting vector was obtained through Total Wavelet Entropy (TWE). In this sense, the presented work propose a viable and practical alert and detection algorithm for muscle fatigue.

Los Angeles machine is used both for mining process and for standard testing covering strength of materials. As the present work is focused on the latter application, an improvement in the estimation procedure for the resistance percentage of small-size coarse aggregate is presented. More precisely, is proposed a pattern identification strategy of the vibratory signal for estimating the resistance percentage using a simplified chaotic model and the continuous wavelet transform.

This paper is a brief review of a new approach to the quantum-chaotic ratchet effect, introduced recently to address for the first time the sensitivity of the effect of the initial state in a global fashion. This is done by studying statistical properties of the ratchet current over well-defined sets of initial states. First results concern the semiclassical full-chaos regime, where the current is strongly sensitive to the initial state. Natural initial states in this regime are those that are phase-space uniform with the maximal possible resolution of the one Planck cell. General arguments, for a class of paradigmatic model systems and for special quantum-resonance values of a scaled Planck constant ħ, predict that the distribution of the momentum current over all such states is a zero-mean Gaussian with variance ~ Dħ²∕(2π²), where D is the chaotic-diffusion coefficient. This prediction is well supported by extensive numerical evidence. The average strength of the effect, measured by the variance above, is significantly larger than that for the usual momentum states and other states. Open problems, concerning extensions of these first results in different directions, are discussed.