2 resultados para Multivariate Equations
em Repositório Digital da UNIVERSIDADE DA MADEIRA - Portugal
Resumo:
This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.
Resumo:
In order to differentiate and characterize Madeira wines according to main grape varieties, the volatile composition (higher alcohols, fatty acids, ethyl esters and carbonyl compounds) was determined for 36 monovarietal Madeira wine samples elaborated from Boal, Malvazia, Sercial and Verdelho white grape varieties. The study was carried out by headspace solid-phase microextraction technique (HS-SPME), in dynamic mode, coupled with gas chromatography–mass spectrometry (GC–MS). Corrected peak area data for 42 analytes from the above mentioned chemical groups was used for statistical purposes. Principal component analysis (PCA) was applied in order to determine the main sources of variability present in the data sets and to establish the relation between samples (objects) and volatile compounds (variables). The data obtained by GC–MS shows that the most important contributions to the differentiation of Boal wines are benzyl alcohol and (E)-hex-3-en-1-ol. Ethyl octadecanoate, (Z)-hex-3-en-1-ol and benzoic acid are the major contributions in Malvazia wines and 2-methylpropan-1-ol is associated to Sercial wines. Verdelho wines are most correlated with 5-(ethoxymethyl)-furfural, nonanone and cis-9-ethyldecenoate. A 96.4% of prediction ability was obtained by the application of stepwise linear discriminant analysis (SLDA) using the 19 variables that maximise the variance of the initial data set.