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Abstract and Applied Analysis
Volume 2014, Article ID 401319, 12 pages
Research Article

Bifurcation Structure in a Bimodal Piecewise Linear Business Cycle Model

1DESP, University of Urbino, Via Saffi 42, 61029 Urbino, Italy
2IST, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
3Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkovskaya Street 3, Kyiv 01601, Ukraine
4Kyiv School of Economics, Ivana Mazepy Street 1, Kyiv 01010, Ukraine
5Department of Economics and Management, University of Pavia, Via S. Felice 5, 27100 Pavia, Italy

Received 17 June 2014; Revised 11 September 2014; Accepted 26 September 2014; Published 19 November 2014

Academic Editor: Jaume Giné

Copyright © 2014 Viktor Avrutin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the bifurcation structure of the parameter space of a 1D continuous piecewise linear bimodal map which describes dynamics of a business cycle model introduced by Day-Shafer. In particular, we obtain the analytical expression of the boundaries of several periodicity regions associated with attracting cycles of the map (principal cycles and related fin structure). By crossing these boundaries the map displays robust chaos.