Dynamical Systems

Medidas invariantes para fluxos de Cherry.

Speaker: 

Edson Vargas

Date: 

Friday, 13 January, 2017 - 14:30

Venue: 

Room M031

Estudamos medidas invariantes para os fluxos de Cherry, isto é: fluxos no toro bidimensional que possuem uma sela, uma fonte, e nenhum outro ponto fixos, órbitas fechadas ou conexões de sela. No caso em que a sela é dissipativa ou conservativa nós mostramos que as únicas medidas invariantes são as medidas de Dirac suportadas nos dois pontos fixos e a medida de Dirac na sela é uma medida física.

Gráficos fractais: regularidade crítica e dimensão

Speaker: 

Katrin Gelfert

Date: 

Friday, 20 January, 2017 - 14:30

Venue: 

Room M031

Estudaremos conjuntos hiperbólicos invariantes de certos produtos tortos com expansão uniforme nas fibras e com difeomorfismos hiperbólicos de superfície na base. Assim, estes conjuntos são gráficos invariantes. Em geral estes gráficos são ou (em casos ``não genéricos") Lipschitz contínuos ou genuinamente Hölder contínuos.  No caso não-Lipschitz sua estrutura fractal é de interesse natural, estudaremos sua dimensão box-counting.

Chaotic flows are abundant

Speaker: 

Paulo Varandas

Date: 

Friday, 11 November, 2016 - 14:30

Venue: 

Room M031

One of the main purposes of dynamical systems is to understand the behavior of the space of orbits of maps and flows on compact metric spaces. It is often the case that we refer to chaotic dynamical systems whenever it presents dense regular behavior (e.g. periodic) and sensitivity to initial conditions.

Using fractional differential equations to model some phenomena

Speaker: 

Nuno Bastos

Date: 

Friday, 4 November, 2016 - 14:30

Venue: 

Room M031

In this talk we deal with fractional differential equations, with dependence on a Caputo fractional derivative. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations [1].

[1] R. Almeida, N.R.O. Bastos and M.T.T. Monteiro,  Modelling some real phenomena by fractional differential equations. Math. Meth. Appl. Sci. (39) No 16, 4846-4855 (2016)

Drug delivery from vehicles and devices: the modelling approach for biomedicine today's challenges

Speaker: 

Giuseppe Pontrelli

Date: 

Thursday, 3 November, 2016 - 14:30

Venue: 

Room M004

In this talk I will present a mathematical model  describing the dynamics of a substance between a two-layer media of different properties and extents. 

The model incorporates drug diffusion, dissolution and solubility  in the polymer coating, coupled with diffusion, convection and reaction in the biological tissue.  Each layer contains bound and free drug phases so that the resulting model is a coupled two-phase two-layer system of partial differential equations. 

Bifurcation of Projected Patterns

Speaker: 

Juliane Oliveira

Date: 

Friday, 28 October, 2016 - 13:30

Venue: 

Room M031

This work is related to the study of pattern formation in symmetric physical systems. Our purpose is to discuss a possible model, namely the projection model, to explain the appearance and evolution of regular patterns in symmetric systems of equations.

  Results found in Crystallography and Equivariant Bifurcation Theory are used extensively in our work. In particular, we provide a formalism of how the model of projection can be used and interpreted to understand experiments of reaction-diffusion systems.

Effective and Anomalous diffusion of tracer and inertial particles in flowing fluids

Speaker: 

Marco Martins Afonso

Date: 

Friday, 30 September, 2016 - 13:30

Venue: 

Room M031

We show some analytical, and partly numerical, results on the effective diffusivity of tracer and inertial particles in flowing fluids. Particle diffusion is a phenomenon where the mean square displacement - after subtracting its average, which corresponds to the advective or ballistic degree of freedom - follows a power law in time. In most standard cases the exponent is 1, and the tensorial prefactor is called "eddy diffusivity" and can be found by means of a multiple-scale expansion. If under investigation are tracers, i.e.

Stochastic Dynamics on Point Processes

Speaker: 

António Sodré

Date: 

Friday, 23 September, 2016 - 13:30

Venue: 

Room M031

Deterministic dynamics on stationary point process in Rd are built upon compatible point-shifts: translation invariant mappings from each point of the process to another. When a point-shift is applied multiple times to a point-process it creates a sequence of distributions, namely, the distributions of point process given there is a point of the nth iteration of the point-shift at the origin. We will introduce the notion of marked stochastic point-shifts.

Multi-bump solutions in a neural field model: analysis and application in cognitive robotics

Speaker: 

Flora Ferreira

Date: 

Friday, 8 July, 2016 - 13:30

Venue: 

Room M031

Stable solutions of an integro-differential equation (known as “Amari equation”) have been proposed as a model of a neural population representation of remembered external stimuli.  In this talk I will present the study of the conditions that guarantee the existence and stability of multiple regions of high activity or ‘‘bumps’’ in a one dimensional, homogeneous neural field with localized inputs. These multi-bump solutions represent the core of an original dynamic field model of fast sequence learning that was developed and tested in a robotics experiment. 

Modeling, stability and optimal control of Tuberculosis and HIV/AIDS models with and without time delay

Speaker: 

Cristiana J. Silva

Date: 

Friday, 1 July, 2016 - 13:30

Venue: 

Room M031

In a first part, we consider a Tuberculosis (TB) model with time delays in both state and control variables, representing the time delay on the diagnosis and commence- ment of treatment of individuals with active TB infection, respectively. The stability of the disease free and endemic equilibriums is investigated for any time delay. Correspon- ding optimal control problems, with time delays in both state and control variables, are formulated and studied. In the second part, we propose a mathematical model for the transmission dynamics of human immunodeficiency virus (HIV).

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