2D discontinuous piecewise linear map: Emergence of fashion cycles

Laura Gardini (), Iryna Sushko () and Kiminori Matsuyama
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Iryna Sushko: Institute of Mathematics, NASU, and Kyiv School of Economics, Ukraine

No 1703, Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini

Abstract: We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are de?ned by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity regions associated with attracting cycles of di?erent periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are obtained analytically in explicit form. We show the existence of several partially overlapping period incrementing structures, that is a novelty for the considered class of maps. Moreover, we show that if the time-delay in the discrete time formulation of the model shrinks to zero, the number of period incrementing structures tends to in?nity and the dynamics of the discrete time fashion cycle model converges to those of continuous-time fashion cycle model.

Keywords: Fashion cycle model; 2D discontinuous piecewise linear map; Border collision bifurcation; Period adding bifurcation structure; Period incrementing bifurcation structure Length: 27 pages (search for similar items in EconPapers)
Date: 2017, Revised 2017
New Economics Papers: this item is included in nep-mac
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