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Bifurcation Curves in Discontinuous Maps

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Author Info

  • Fabio Tramontana

    ()
    (Università Politecnica delle Marche & Dipartimento di Economia e Metodi Quantitativi, Università di Urbino)

  • Laura Gardini

    ()
    (Dipartimento di Economia e Metodi Quantitativi, Università di Urbino (Italy))

  • Gian Italo Bischi

    ()
    (Dipartimento di Economia e Metodi Quantitativi, Università di Urbino (Italy))

Abstract

Several discrete-time dynamic models are ultimately expressed in the form of iterated piecewise linear functions, in one or two-dimensional spaces. In this paper we study a one-dimensional map made up of three linear pieces which are separated by two discontinuity points, motivated by a dynamic model arising in social sciences. Starting from the bifurcation structure associated with one-dimensional maps with only one discontinuity point, we show how this is modi ed by the introduction of a second discontinuity point, and we give the analytic expressions of the bifurcation curves of the principal tongues (or tongues of first degree), for the family of maps considered, that depends on five parameters.

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File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_08_05.pdf
File Function: First version, 2008
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Bibliographic Info

Paper provided by University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini in its series Working Papers with number 0805.

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Length: 22 pages
Date of creation: 2008
Date of revision: 2008
Handle: RePEc:urb:wpaper:08_05

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Web page: http://www.econ.uniurb.it/
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Keywords: iterated piecewise linear functions; discrete-time dynamic models; bifurcation curves.;

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