Quantifying chaos for ecological stoichiometry

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincareacute return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing delta(1). However, for higher values of delta(1) the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter zeta) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K, C-0) and (K, sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K-c decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

Preferências no exercício físico em mulheres portuguesas sobreviventes de cancro da mama

Introdução – Os benefícios do exercício físico em sobreviventes de cancro da mama têm sido reportados; contudo, a sua prática permanece baixa, tornando importante o conhecimento dos fatores que promovam a motivação e adesão ao exercício nesta população. Objetivos – Identificar as preferências quanto à programação e aconselhamento do exercício físico de uma amostra da população de mulheres portuguesas sobreviventes de cancro da mama e averiguar a influência das variáveis demográficas e médicas nestas preferências. Método – Foi aplicado um questionário a uma amostra não probabilística sequencial de 26 mulheres sobreviventes de cancro da mama. Resultados – A amostra era maioritariamente constituída por mulheres entre os 45 e os 62 anos, casadas ou em união de facto, com ensino básico, empregadas e com Índice de Massa Corporal (IMC) > 24,4. Maioritariamente tinham realizado cirurgia radical há um mês ou mais, apresentavam estadio I do tumor, efetuavam quimioterapia como tratamento adjuvante e algumas realizavam classes de fisioterapia. A maioria das participantes demonstrava interesse em receber aconselhamento, sentia-se apta a participar num programa de exercício, preferia receber aconselhamento face-a-face no hospital e acompanhada por outros doentes oncológicos. O exercício deveria ser supervisionado e com intensidade moderada, sendo as caminhadas o tipo de exercício preferido. Não foi estatisticamente possível realizar a associação entre as variáveis demográficas e médicas e as preferências. Conclusão – Alguns resultados obtidos estão em concordância com estudos prévios; contudo, outros divergem destes. Os resultados obtidos podem fornecer informações importantes para a construção futura de programas de exercício para esta população. ABSTRACT - Introduction – The benefits of physical exercise in cancer survivors have been reported, although it’s practice remains low, becoming important the acknowledgement of the factors that promote the motivation and adhesion of physical exercise in this population. Objectives – To identify the preferences about programming and counseling of physical exercise inside a population-based sample of Portuguese women who have survived breast cancer. We also intend to investigate the influence of demographic and medical variables in those preferences. Method – A questionnaire was applied to a non-probabilistic sequential sample of 26 women that have survived breast cancer. Results – Our sample was mainly composed by women aged between 45 and 62, married or in a cohabitation state, with basic instruction, employed and with a Body Mass Index (BMI)> 24.4. Most of them have had radical mastectomy for at least one month, had the Stage I of the tumor, and had done chemotherapy as an adjuvant treatment and some of them were practicing post-surgery physical therapy. The majority of participants showed interest in receiving counseling, felt able to participate in an exercise program, preferred receiving face-to-face counseling, at the hospital and with other cancer patients. The exercise should be supervised and with a moderate intensity. Walking was their preferred choice of exercise. It was not statistically possible to establish the relationship between demographic and medical variables and those preferences. Conclusion – Some results are in agreement with previous studies; however, others diverge from these. The results obtained can provide important information for future construction of exercise programs for this population.

Fundos de investimento imobiliário

Mestrado em Contabilidade e Gestão das Instituições Financeiras