Malthus e a Evolução de Modelos

There is usually a correlation between the development of a mathematical model and the evolution of mathematics. This statement is more evident when dealing with mathematical models of some reality. The study of population dynamics gives an idea of the evolutionary process of mathematical models. The Malthus postulated that initially showed an exponential population growth led to the formulation of models with inhibited growth. Currently, new techniques and mathematical concepts provide new models – it is the case of fuzzy theory, cellular automata and coupled dynamical systems.Existe, via de regra, uma correspondência entre a evolução de um modelo matemático e a própria evolução da matemática. Esta afirmação é mais evidente quando tratamos de modelos matemáticos de alguma realidade. O estudo da dinâmica populacional dá uma idéia do processo evolutivo dos modelos matemáticos. Os postulados de Malthus que indicavam inicialmente um crescimento populacional exponencial deram origem à formulação de modelos com crescimento inibido.  Atualmente, novas técnicas e conceitos matemáticos propiciam novos modelos – é o caso da Teoria fuzzy, dos autômatos celulares e dos sistemas dinâmicos acoplados

Sobre o problema de Dirichlet n-dimensional para equação das superficies minimas em dominios com fronteira singular

Orientador : Ubiratan D'AmbrosioTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Não informado.Abstract: Not informed.DoutoradoDoutor em Matemátic

Methodology to determine the evolution of asymptomatic HIV population using fuzzy set theory

The aim of this paper is to o study the evolution of positive HIV population for manifestation of AIDS, the Acquired Immunodeficiency Syndrome. For this purpose, we suggest a methodology to combine a macroscopic HIV positive population model with an individual microscopic model. The first describes the evolution of the population whereas the second the evolution of HIV in each individual of the population. This methodology is suggested by the way that experts use to conduct public policies, namely, to act at the individual level to observe and verify the manifest population. The population model we address is a differential equation system whose transference rate from asymptomatic to symptomatic population is found through a fuzzy rule-based system. The transference rate depends on the CD4+ level, the main T lymphocyte attacked by the HIV retrovirus when it reaches the bloodstream. The microscopic model for a characteristic individual in a population is used to obtain the CD4+ level at each time instant. From the CD4+ level, its fuzzy initial value, and the macroscopic population model, we compute the fuzzy values of the proportion of asymptomatic population at each time instant t using the extension principle. Next, centroid defuzzification is used to obtain a solution that represents the number of infected individuals. This approach provides a method to find a solution of a non-autonomous differential equation from an autonomous equation, a fuzzy initial value, the extension principle, and center of gravity defuzzification. Simulation experiments show that the solution given by the method suggested in this paper fits well to AIDS population data reported in the literature.The aim of this paper is to o study the evolution of positive HIV population for manifestation of AIDS, the Acquired Immunodeficiency Syndrome. For this purpose, we suggest a methodology to combine a macroscopic HIV positive population model with an indiv1313958CAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOSEM INFORMAÇÃO304299/2003-

A first course in fuzzy logic, fuzzy dynamical systems, and biomathematics: theory and applications

This book provides an essential introduction to the field of dynamical models. Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. On one hand, the book equips readers with a fundamental understanding of the theoretical underpinnings of fuzzy sets and fuzzy dynamical systems. On the other, it demonstrates how these theories are used to solve modeling problems in biomathematics, and presents existing derivatives and integrals applied to the context of fuzzy functions. Each of the major topics is accompanied by examples, worked-out exercises, and exercises to be completed. Moreover, many applications to real problems are presented. The book has been developed on the basis of the authors’ lectures to university students and is accordingly primarily intended as a textbook for both upper-level undergraduates and graduates in applied mathematics, statistics, and engineering. It also offers a valuable resource for practitioners such as mathematical consultants and modelers, and for researchers alike, as it may provide both groups with new ideas and inspirations for projects in the fields of fuzzy logic and biomathematics

Predator-prey fuzzy model

In this work we have used fuzzy rule-based systems to elaborate a predator-prey type of model to study the interaction between aphids (preys) and ladybugs (predators) in citriculture, where the aphids are considered as transmitter agents of the Citrus Sudden Death (CSD). Simulations were performed and a graph was drawn to show the prey population, the potentiality of the predators, and a phase-plane. From this phase-plane, a classic model of the Holling-Tanner type is fitted and its parameters were found. Finally, we have studied the stability of the critical points of the Holling-Tanner model. © 2008 Elsevier B.V. All rights reserved.In this work we have used fuzzy rule-based systems to elaborate a predator-prey type of model to study the interaction between aphids (preys) and ladybugs (predators) in citriculture, where the aphids are considered as transmitter agents of the Citrus Sud21413944CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOSEM INFORMAÇÃOBassanezi, R.B., Bergamin Filho, A., Amorim, L., Gimenes-Fernandes, N., Gottwald, T.R., Spatial and temporal analysis of Citrus Sudden Death as a tool to generate hypothesis its etiology (2003) Phytopathology, 93, pp. 502-512Braga, A., Sousa-Silva, C.R., (1999) Afídeos de citros (Citrus sinensis) e seus predadores na região de São Carlos-SP, , Departamento de Ecologia e Biologia Evolutiva da Universidade Federal de São Carlos, São Carlos/SP, BrazilEdelstein-Keshet, L., (1987) Mathematical Models in Biology, , McGraw-Hill, IncGravena, S., O controle biológico na cultura algodoeira (2003) Informe Agropecuário, 9, pp. 3-15Hodek, I., Biology of Coccinellidae (1973) Prague: Academic of ScienceHsin, C., Yang, T., Two-sex life table and predation rate of Propylaea japonica Thunberg (Coleoptera: Coccinellidae) fed on Myzus persicae (Sulzer) (Homoptera: Aphididae) (2003) Environ. Entomol., 32 (2), pp. 327-333Jafelice, R.M., Barros, L.C., Bassanezi, R.C., Gomide, F., Fuzzy modeling in symptomatic HIV virus infected population (2003) Bull. Math. Biol., 66, pp. 1597-1620Klir, G., Yuan, B., (1995) Fuzzy Sets and Fuzzy Logic-Theory and Application, , Prentice HallMorales, J., Buranr Jr., V., Interactions between Cycloneda sanhuine and the brown citrus aphid: adult feeding and larval mortality (1985) Environ. Entomol., 14 (4), pp. 520-522Murray, J., (1990) Mathematical Biology, , Springer, BerlinPeixoto, M.S., 2005. Sistemas Dinâmicos e Controladores Fuzzy: um Estudo da Dispersão da Morte Súbita dos Citros em São Paulo. Ph.D. Thesis. IMECC-UNICAMP, Campinas/SP, BrazilPeixoto, M.S., Barros, L.C., Bassanezi, R.C., Predator-prey fuzzy model in citrus: aphids and ladybugs (2005) Proceedings of the Fourth Brazilian Symposium on Mathematical and Computational Biology/First International Symposium on Mathematical and Computational Biology, I, pp. 228-239.Pedrycz, W., Gomide, F., (1998) An Introduction to Fuzzy Sets: Analysis and Design, , Massachusetts Institute of TechnologySvirezhev, Y.M., Logofet, D.O., (1983) Stability of Biological Communities, , MIR Publishers, MoscowTanner, J.T., The stability and the intrinsic growth rates of prey and predator populations (1975) Ecology, 56, pp. 855-867Zadeh, L.A., Fuzzy sets (1965) Inform. Control, 8, pp. 338-35