Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.13/206
Título: Nonautonomous difference equations with applications
Autor: Luís, Rafael Domingos Garanito
Palavras-chave: Nonautonomous periodic systems
Competition Models
Allee effect
Centro de Ciências Exatas e da Engenharia
Data de Defesa: 2011
Editora: Universidade da Madeira
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.
Peer review: yes
URI: http://hdl.handle.net/10400.13/206
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