Dynamic headspace solid-phase microextraction combined with one-dimensional gas chromatography–mass spectrometry as a powerful tool to differentiate banana cultivars based on their volatile metabolite profile

In this study the effect of the cultivar on the volatile profile of five different banana varieties was evaluated and determined by dynamic headspace solid-phase microextraction (dHS-SPME) combined with one-dimensional gas chromatography–mass spectrometry (1D-GC–qMS). This approach allowed the definition of a volatile metabolite profile to each banana variety and can be used as pertinent criteria of differentiation. The investigated banana varieties (Dwarf Cavendish, Prata, Maçã, Ouro and Platano) have certified botanical origin and belong to the Musaceae family, the most common genomic group cultivated in Madeira Island (Portugal). The influence of dHS-SPME experimental factors, namely, fibre coating, extraction time and extraction temperature, on the equilibrium headspace analysis was investigated and optimised using univariate optimisation design. A total of 68 volatile organic metabolites (VOMs) were tentatively identified and used to profile the volatile composition in different banana cultivars, thus emphasising the sensitivity and applicability of SPME for establishment of the volatile metabolomic pattern of plant secondary metabolites. Ethyl esters were found to comprise the largest chemical class accounting 80.9%, 86.5%, 51.2%, 90.1% and 6.1% of total peak area for Dwarf Cavendish, Prata, Ouro, Maçã and Platano volatile fraction, respectively. Gas chromatographic peak areas were submitted to multivariate statistical analysis (principal component and stepwise linear discriminant analysis) in order to visualise clusters within samples and to detect the volatile metabolites able to differentiate banana cultivars. The application of the multivariate analysis on the VOMs data set resulted in predictive abilities of 90% as evaluated by the cross-validation procedure.

Nonautonomous difference equations with applications

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.