Modelo de Lotka-Volterra com inclusão de termos perturbativos e capacitivos

Our purpose is to show the effects in the predator-prey trajectories due to parameter temporal perturbations and/or inclusion of capacitive terms in the Lotka Volterra Model. An introduction to the Lotka Volterra Model (chapter 2) required a brief review of nonlinear differential equations and stability analysis (chapter 1) , for a better understanding of our work. In the following chapters we display in sequence our results and discussion for the randomic pertubation case (chapter 3); periodic perturbation (chapter 4) and inclusion of capacitive terms (chapter 5). Finally (chapter 6) we synthesize our result

Estudo das propriedades dinâmicas e sincronização no mapa de rede de Zaslavsky

Synchronization in nonlinear dynamical systems, especially in chaotic systems, is field of research in several areas of knowledge, such as Mechanical Engineering and Electrical Engineering, Biology, Physics, among others. In simple terms, two systems are synchronized if after a certain time, they have similar behavior or occurring at the same time. The sound and image in a film is an example of this phenomenon in our daily lives. The studies of synchronization include studies of continuous dynamic systems, governed by differential equations or studies of discrete time dynamical systems, also called maps. Maps correspond, in general, discretizations of differential equations and are widely used to model physical systems, mainly due to its ease of computational. It is enough to make iterations from given initial conditions for knowing the trajectories of system. This completion of course work based on the study of the map called ”Zaslavksy Web Map”. The Zaslavksy Web Map is a result of the combination of the movements of a particle in a constant magnetic field and a wave electrostatic propagating perpendicular to the magnetic field. Apart from interest in the particularities of this map, there was objective the deepening of concepts of nonlinear dynamics, as equilibrium points, linear stability, stability non-linear, bifurcation and chaos

Modelagem matemática de tumores e estequiometria biológica

Cancer biology is a complex and expanding field of science study. Due its complexity, there is a strong motivation to integrate many fields of knowledge to study cancer biology, and biological stoichiometry can make this. Biological stoichiometry is the study of the balance of multiple chemical elements in biological systems. A key idea in biological stoichiometry is the growth rate hypothesis, which states that variation in the carbon:nitrogen:phosphorus stoichiometry of living things is associated with growth rate because of the elevated demands for phosphorusrich ribosomal RNA and other elements necessary to protein synthesis. As tumor cells has high rate proliferation, the growth rate hypothesis can be used in cancer study. In this work the dynamic of two tumors (primary and secondary) and the chemical elements carbon and nitrogen are simulate and analyzed through mathematical models that utilize as central idea biological stoichiometry. Differential equations from mathematical model are solved by numerical method Runge-Kutta fourth order

Estudo de placas com várias condições de contorno e de carregamento através do método dos elementos de contorno

Even today tables are used in the calculation of structures formed by flat elements, these methods are acceptable only for a limited number of cases, but even so, in some situations, tables are used. With time some methods of differential equations resolutions were emerging and accepted as the most effective solution. Today, with the advancement in technology, there are already some programs able to solve more complex problems in less time using these methods. Aiming to optimize time and better understand the physical behavior of plates, this work presents the theory of plate, the Boundary Element Method (BEM) applied to solve problems of plates (slabs) with various boundary conditions and load through the program Placas2 (TAGUTI, Y.-2010) in Fortran language

Simulação numérica de fluxo de águas subterrâneas na fazenda Cara Preta - Santa Rita do Passa Quatro - SP

The term model refers to any representation of a real system. The use of models in Hydrogeology can be valuable predictive tools for management of groundwater resources. The numeric models of groundwater flow, object of this study, consist on a set of differential equations that describe the water flow in the porous medium. In this context, numeric simulations were made for a sub-basin located at Cara Preta farm – Santa Rita do Passa Quatro – SP. The aquifer at the local is composed by rocks of Pirambóia Formation, which is part of Guarani Aquifer System. It was developed a conceptual model from previous studies in the area, and from that, simulations were made through the software Visual Modflow®. The conceptual model established previously was considered consistent through the results of simulation.

Algoritmo de resolução de EDO de primeira ordem com implementação em HTML

This work presents a theoretical study of ordinary differential equations of first order directed so as to provide basis for the development of an educational software that helps students and researchers confronted with this issue. The algorithm was developed in HTML language in to that the results provide a website that allows the audience to access the software anywhere which has internet connection

Análise da estabilidade do movimento rotacional de satélites artificiais com quatérnions e sob a influência de torques externos

The aim of this work is to analyze the stability of the rotational motion’s artificial satellite using the Routh Hurwitz Algorithm (CRH) and the quaternions to describe the satellite’s attitude. This algorithm allows the investigation of the stability of the motion using the coefficients of the characteristic equation associated with the equation of the rotational motion in the linear form. The equations of the rotational motion are given by the four cinematic equations for the quaternion and the three equations of Euler for the spin velocity’s components. In the Euler equations are included the components of the gravity gradient torque (TGG) and the solar radiation torque (TRS). The TGG is generated by the difference of the Earth gravity force direction and intensity actuating on each satellite mass element and it depends on the mass distribution and the form of the satellite. The TRS is created by changing of the linear momentum, which happens due to the interactions of solar photons with the satellite surface. The equilibrium points are gotten by the equation of rotational motion and the CRH is applied in the linear form of these equations. Simulations are developed for small and medium satellites, but the gotten equilibrium points are not stable by CRH. However, when some of the eigenvalues of the characteristic equation are analyzed, it is found some equilibrium points which can be pointed out as stables for an interval of the time, due to small magnitude of the real part of these eigenvalue

Estudo e aplicação de diferentes métodos de resolução para problemas dinâmicos não-lineares em presença de atrito

The friction phenomena is present in mechanical systems with two surfaces that are in contact, which can cause serious damage to structures. Your understanding in many dynamic problems became the target of research due to its nonlinear behavior. It is necessary to know and thoroughly study each existing friction model found in the literature and nonlinear methods to define what will be the most appropriate to the problem in question. One of the most famous friction model is the Coulomb Friction, which is considered in the studied problems in the French research center Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC), where this search began. Regarding the resolution methods, the Harmonic Balance Method is generally used. To expand the knowledge about the friction models and the nonlinear methods, a study was carried out to identify and study potential methodologies that can be applied in the existing research lines in LMSSC and then obtain better final results. The identified friction models are divided into static and dynamic. Static models can be Classical Models, Karnopp Model and Armstrong Model. The dynamic models are Dahl Model, Bliman and Sorine Model and LuGre Model. Concerning about nonlinear methods, we study the Temporal Methods and Approximate Methods. The friction models analyzed with the help of Matlab software are verified from studies in the literature demonstrating the effectiveness of the developed programming

Caracterização e redução das oscilações espúrias resultantes da representação de linhas de transmissão por meio de elementos discretos de circuitos

Pós-graduação em Engenharia Elétrica - FEIS

epresentação de linhas de transmissão por meio do modelo de bergeron: inclusão do efeito da frequência nos parâmetros longitudinais

Pós-graduação em Engenharia Elétrica - FEIS

Identificação de forças de excitação em sistemas rotativos utilizando funções ortogonais

Pós-graduação em Engenharia Mecânica - FEIS

Controle Ótimo Aplicado em um Modelo de Câncer

Pós-graduação em Matematica Aplicada e Computacional - FCT

Equação de Fokker-Planck e enovelamento de proteínas

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

Relaxação e decaimento para pontos de equilíbrio em mapeamentos não lineares unidimensionais

We investigate in this work the behaviour of the decay to the fixed points, in particular along the bifurcations, for a family of one-dimensional logistic-like discrete mappings. We start with the logistic map focusing in the transcritical bifurcation. Next we investigate the convergence to the stationary state at the cubic map. At the end we generalise the procedure for a mapping of the logistic-like type. Near the fixed point, the dynamical variable varies slowly. This property allows us to approximate/rewrite the equation of differences, hence natural from discrete mappings, into an ordinary differential equation. We then solve such equation which furnishes the evolution towards the stationary state. Our numerical simulations confirm the theoretical results validating the above mentioned approximation

Modelos matemáticos e computacionais para descrever a transmissão de dois sorotipos de vírus de dengue

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)