Analytical and numerical results for detecting attractors

摘要

In this paper we present some qualitative and quantitative results for a particular type of k-order exchange rate models. These results concern the existence of attractors: the fixed point, its stability and its attraction domain, period-p cycles, limit cycles and chaotic attractors. Given the nonlinear nature, the dynamics of these systems cannot be detected using only analytical tools. For this reason, in the last section, we make numerical simulations and we present some examples. The algorithms implementation is made using VBA (Visual Basic for Applications) program in Excel, and the images of the figures in this paper are made using Mathematica.