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Bifurcations

In: Nonlinearities in Economics

Author

Listed:
  • Giuseppe Orlando

    (University of Bari, Department of Economics and Finance
    University of Camerino, School of Sciences and Technology)

  • Ruedi Stoop

    (ETHZ/University of Zürich)

  • Giovanni Taglialatela

    (University of Bari, Department of Economics and Finance)

Abstract

Many dynamical systems depend on parameters. One may expect that small variations of the parameters produce no significant changes in the orbits. As was shown in Chap. 3 for the Logistic Map, even in simple cases, there exist critical values such that, moving the parameters through them, the orbits can change dramatically. In the present chapter, we first provide the definition of homoclinic and heteroclinic orbits and then a summary about local bifurcations for both the continuous case and the discrete-time case. Global bifurcations will be presented in the next following chapter.

Suggested Citation

  • Giuseppe Orlando & Ruedi Stoop & Giovanni Taglialatela, 2021. "Bifurcations," Dynamic Modeling and Econometrics in Economics and Finance, in: Giuseppe Orlando & Alexander N. Pisarchik & Ruedi Stoop (ed.), Nonlinearities in Economics, chapter 0, pages 51-72, Springer.
    • Handle: RePEc:spr:dymchp:978-3-030-70982-2_4
    DOI: 10.1007/978-3-030-70982-2_4
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