Resumo. A produção de cana-de-açúcar no Brasil é um importante setor do agronegócio. Ela é matéria-prima para a produção de biocombistíveis, bioplásticos, bioenergia, bebidas e alimentos. Nas últimas décadas, com a expansão das plantações e a proibição das queimadas, houve um aumento significativo na população de pragas, sendo a broca da cana-de-açúcar, Diatraea saccharalis, a principal delas. Essa praga cava galerias internas nos colmos das plantas causando prejuízos, diminuindo a qualidade e o rendimento industrial. Dessa forma, o propósito deste trabalho é estudar a interação entre a broca da cana-de-açúcar, primeiramente, com seu parasitoide larval, Cotesia flavipes e na sequência, incluindo também o seu parasitoide do ovo, Trichogramma galloi, que demonstram desempenho satisfatório no controle biológico da broca da cana-de-açúcar. A interação entre essas populações é modelada por sistemas do tipo parasitoide-hospedeiro, para o qual é feito o estudo considerando os parâmetros constantes e também com a variação sazonal. As simulações mostram que a inclusão da variação sazonal nos dois sistemas altera a dinâmica, podendo gerar comportamento caótico.Palavras-chave. Broca da cana-de-açúcar, Cotesia flavipes, Trichogramma galloi, Sazonalidade.
Sugarcane production is a significant and profitable agribusiness sector in many countries. Nevertheless, this industry suffers significant losses from the sugarcane pests, among which the most important one is the sugarcane borer (Diatraea saccharalis). This pest population is hard to be controlled due to its different life stages, thus biological control ( with more than one predator species) can be applied. Therefore, in this work, we present and analyze a mathematical model that describes the dynamics of the sugarcane borer and its two different life stages parasitoids: eggs (Trichogramma galloi) and larval (Cotesia flavipes). First, a host-parasitoid model is used to obtain the population dynamics, which also considers the influence of seasonal variations. Then, system simulations and bifurcation diagrams show that the introduction of seasonality perturbations causes complex dynamics and results in limit cycles and strange attractors.
High failure rates in the Differential and Integral Calculus courses and the subsequent dropout caused by them are a reason for concern in many universities around the world, both in developing countries such as Brazil and developed ones such as the United States of America. So, it is not surprising that there is lots of interest in researching about this context, and possible ways of action. This is the focus of this article, to study about the origins of this situation, analyzing the causes of the students’ difficulties and presenting Collaborative Learning as an effective way to change this situation. The article is based on data from several universities that have shown interest in this method. The results demonstrate the effectiveness of this practice, both in academic and psychological performance of the students, thus showing the need for a greater incentive of this technique, as well as an intense study of the way it should be done.
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