Bifurcation Curves in Discontinuous Maps

Fabio Tramontana, Laura Gardini () and Gian Italo Bischi

No 805, Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini

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.

Keywords: iterated piecewise linear functions; discrete-time dynamic models; bifurcation curves. (search for similar items in EconPapers)
JEL-codes: C02 C62 C63 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2008, Revised 2008
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