Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus

Modeling Allee Effect from Beta(p, 2) Densities

In this work we develop and investigate generalized populational growth models, adjusted from Beta(p, 2) densities, with Allee effect. The use of a positive parameter leads the presented generalization, which yields some more flexible models with variable extinction rates. An Allee limit is incorporated so that the models under study have strong Allee effect

Reflecting On the Past; Shaping the Future of Student Affairs

The purpose of this essay is to invite student affairs educators to reflect on the past to help shape the future of the profession. The metaphor of a public art exhibit with five reflective questions is used to inspire educators to think critically about student engagement. As the demographics of students pursuing higher education changes, we urge a recommitment to historically underserved student populations. This call to service invokes a social justice philosophy when we serve historically marginalized student groups, including immigrants, students of color, and first-generation learners. Doing so will engage students and reenergize our commitment to the profession

Synchronization in Von Bertalanffy’s models

Many data have been useful to describe the growth of marine mammals, invertebrates and reptiles, seabirds, sea turtles and fishes, using the logistic, the Gom-pertz and von Bertalanffy's growth models. A generalized family of von Bertalanffy's maps, which is proportional to the right hand side of von Bertalanffy's growth equation, is studied and its dynamical approach is proposed. The system complexity is measured using Lyapunov exponents, which depend on two biological parameters: von Bertalanffy's growth rate constant and the asymptotic weight. Applications of synchronization in real world is of current interest. The behavior of birds ocks, schools of fish and other animals is an important phenomenon characterized by synchronized motion of individuals. In this work, we consider networks having in each node a von Bertalanffy's model and we study the synchronization interval of these networks, as a function of those two biological parameters. Numerical simulation are also presented to support our approaches

Dynamical behaviour on the parameter space: new populational growth models proportional to beta densities

We present new populational growth models, generalized logistic models which are proportional to beta densities with shape parameters p and 2, where p > 1, with Malthusian parameter r. The complex dynamical behaviour of these models is investigated in the parameter space (r, p), in terms of topological entropy, using explicit methods, when the Malthusian parameter r increases. This parameter space is split into different regions, according to the chaotic behaviour of the models

Generalized Ladder Operators for Shape-invariant Potentials

A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.Comment: in Revte

CONHECIMENTO E ACESSO À INFORMAÇÃO SOBRE O PAPEL DA PRAIA NA PROTEÇÃO DA COSTA

Em todo o mundo, as zonas costeiras exercem forte atração para a fixação humana, em razão de seus atrativos paisagísticos ou econômicos, o que torna esses os lugares de maior concentração populacional em todo o planeta. Desconsiderando, ou até mesmo desconhecendo, as características naturais próprias deste tipo de ambiente, a ocupação antrópica, em muitas ocasiões, dá-se de forma desordenada e imprópria. Os habitantes dessas zonas ficam, assim, suscetíveis às constantes variações morfodinâmicas desses ambientes. Em muitos países adota-se nessas áreas o estabelecimento de faixa de proteção ou de restrição de uso visando prevenir perdas e danos materiais decorrentes da erosão costeira, bem como evitar a alteração da paisagem característica desses locais. No Brasil, o Plano Nacional de Gerenciamento Costeiro (Projeto Orla) busca disciplinar o uso e a ocupação dos espaços e recursos da orla marítima, orientando o poder público e a sociedade a definirem e decidirem sobre o que deve e o que não deve ser feito nesse espaço. O presente trabalho teve como objetivo confeccionar um documento sobre processos costeiros necessário para o entendimento e a participação da comunidade civil na implantação do Projeto Orla e/ou a participação crítica do cidadão sobre as ações realizadas em praias e costas. Entrevistas realizadas com usuários de praia demonstraram que esse público possui algum nível de entendimento correto sobre o ambiente praial, mas, ficou evidente que há importantes lacunas de conhecimento quanto ao espaço costeiro que carecem de instrução, o desconhecimento de que a praia pode proteger a orla em caso de uma possível subida do nível do mar é uma delas. O levantamento de informações disponíveis na internet, sobre a dinâmica da área costeira, revelou que o material que o leitor leigo no assunto pode acessar, ler e compreender é, de maneira geral, insuficiente ou superficial e pouco esclarece sobre os processos naturais da zona costeira, tampouco, que parte da erosão que a população vive está associada à vulnerabilidade de uso. Notou-se que o nível de informação veiculada pela mídia em geral, não permite que se chegue a tal conclusão, o que demonstrou ser insuficiente. Apresentou-se, neste trabalho, a divulgação dessas informações de maneira adequada e com vocabulário acessível ao cidadão comum através de material disponível em mídia impressa (cartilha) e pela web (blog) que possibilitam ao cidadão comum uma iniciação no assunto e a possibilidade de discutir criticamente sobre ações determinadas para a orla marítima

An Algebraic q-Deformed Form for Shape-Invariant Systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserve the shape-invariance property presented by primary system. q-deformed generalizations of Morse, Scarf, and Coulomb potentials are given as examples