Coexisting Attractors and Complex Basins in Discrete-time Economic Models

Abstract

In this lesson we consider discrete time dynamical systems with coexisting attractors, and we analyze the problem of the structure of the boundaries that separate their basins of attraction. This problem may become particularly challenging when the discrete dynamical system is represented by the iteration of a noninvertible map, because in this case nonconnected basins can be obtained, formed by several (even infinitely many) disjoint portions. Measure theoretic attractors, known as Milnor attractors, are also described, together with riddled basins, an extreme form of complex basin’s structure that can be observed in the presence of such attractors. Some tools for the study of global bifurcations that lead to the creation of complex structures of the basins are described, as well as some applications in discrete time models taken from economic dynamics.