Síntese de dinâmica não-linear por meio de modelos afins por partes: um método baseado em topologia

Abstract

Nonlinear dynamics are inherent to the majority of the systems. Therefore, the study and analysis of such systems it is a reality in most diverse branches of sciences, from pure mathematics to applied sciences as engineering. A common challenge of sciences is to built models that express some characteristics of interest in the system. From such models the original system can be better understood. However, the building of models that express nonlinear dynamic systems representatively continues being an open challenge. This work investigates how the topological characteristics and dynamics of a nonlinear dynamical system can help in the vector field reconstruction in the three-dimension phase space. It is shown by some examples that the achieved models are parsimonious and moreover that, they reproduce the global behavior of the system keeping the local properties. To guarantee formal equivalence tools of topological analysis are used. The main objective of this work is the nonlinear dynamic synthesis by means of piecewise affine models. In this direction an orientation based on the topological structure of strange attractors is developed so that piecewise affine models can be constructed. Also the work explores the relation between switching surface of the models and the system bifurcation parameters. Since such representative models are parsimonious, electronic circuits that implement the dynamics were developed and tested.