Measuring complexity in a business cycle

The purpose of this paper is to study the dynamical behavior of a family of two- dimensional nonlinear maps associated to an economic model. Our objective is to measure the complexity of the system using techniques of symbolic dynamics in order to compute the topological entropy. The analysis of the variation of this im- portant topological invariant with the parameters of the system, allows us to distin- guish different chaotic scenarios. Finally, we use a another topological invariant to distinguish isentropic dynamics and we exhibit numerical results about maps with the same topological entropy. This work provides an illustration of how our under- standing of higher dimensional economic models can be enhanced by the theory of dynamical systems

Hunting Admissible Kneading pairs of a Real Rational Map

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.The importance of symbolic systems is that they give us the possibility of simplifying some dynamical systems. Our expectations is that our work can help to understand better the behavior, under iteration, of the Real Rational Map, f(x)=(x²-a)/(x²-b), with 0<b<a<1. Kneading Theory is a powerful tool, and we use it to simplify processes arising from the complicated behavior of this map in a more simple way. In this work we establish some rules that bound regions where we can find, or not, Kneading pairs for f(x)

Bifurcations and chaos generation from 1D or 2D circuits

none3openD. Fournier-Prunaret; P. Chargé; L. GardiniD., Fournier Prunaret; P., Chargé; Gardini, Laur