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Tongues of periodicity in a family of two-dimensional discontinuous maps of real Mobius type
National Academy of Sciences Ukraine, Math Inst.
University of Urbino, Dept Economics, Urbino.
Umeå University, Faculty of Social Sciences, Centre for Regional Science (CERUM).
2004 (English)In: Chaos, Solitons & Fractals, ISSN 0960-0779, Vol. 21, no 2, 403-412 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we consider a two-dimensional piecewise-smooth discontinuous map representing the so-called "relative dynamics" of an Hicksian business cycle model. The main features of the dynamics occur in the parameter region in which no fixed points at finite distance exist, but we may have attracting cycles of any periods. The bifurcations associated with the periodicity tongues of the map are studied making use of the first-return map on a suitable segment of the phase plane. The bifurcation curves bounding the periodicity tongues in the parameter plane are related with saddle-node and border-collision bifurcations of the first-return map. Moreover, the particular "sausages structure" of the bifurcation tongues is also explained.

Place, publisher, year, edition, pages
2004. Vol. 21, no 2, 403-412 p.
Keyword [en]
bifurcations, cycles, trade
National Category
Economics
Identifiers
URN: urn:nbn:se:umu:diva-13791DOI: 10.1016/j.chaos.2003.12.012OAI: oai:DiVA.org:umu-13791DiVA: diva2:153462
Available from: 2008-03-31 Created: 2008-03-31 Last updated: 2009-07-02Bibliographically approved

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