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Coexisting Attractors and Complex Basins in Discrete-time Economic Models

  • Gian Italo Bischi
  • Fabio Lamantia
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 476)

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.

Keywords

Nash Equilibrium Chaotic Attractor Global Bifurcation Discrete Dynamical System Basin Boundary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© CISM, Udine 2005

Authors and Affiliations

  • Gian Italo Bischi
    • 1
  • Fabio Lamantia
    • 2
  1. 1.Istituto di Scienze EconomicheUniversity of UrbinoUrbinoItaly
  2. 2.S.A. DepartmentUniversity of CalabriaArcavacata di Rende (CS)Italy

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