Isentropic dynamics and control in an economic model for capital accumulation

Abstract

The study of economic models has generated deep interest in exploring the complexity of our society. The primary purpose of this article is to study the chaotic dynamical behavior of an economic growth model describing capital accumulation presented by Bohm and Kaas in [3]. To start with, we use the techniques of symbolic dynamics to explore several properties, with the explicit computation of two topological invariants, which are associated with the discrete dynamical system in consideration. The analysis of these results allows us to understand the dynamics of the economical model and to distinguish different scenarios of complexity, namely in situations of isentropic dynamics. Finally, we show that the chaotic behavior arising from the discrete model can be controlled without changing its original properties and the dynamics can be turned into a desired attracting time periodic motion (a stable steady state or a regular cycle). The orbit stabilization is illustrated by a analytical control technique. This study tends to integrate and interrelate different methods in order to illustrate how our understanding of economic models can be enhanced by the theory of nonlinear dynamical systems.