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Bifurcation Curves in Discontinuous Maps


  • 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))


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.

Suggested Citation

  • Fabio Tramontana & Laura Gardini & Gian Italo Bischi, 2008. "Bifurcation Curves in Discontinuous Maps," Working Papers 0805, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
  • Handle: RePEc:urb:wpaper:08_05

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    More about this item


    iterated piecewise linear functions; discrete-time dynamic models; bifurcation curves.;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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