Measuring complexity in a business cycle

Abstract

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.