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Tongues of periodicity in a family of two-dimensional discontinuous maps of real Möbius type
Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine.
Department of Economics, University of Urbino, Italy.
Umeå University, Faculty of Social Sciences, Centre for Regional Science (CERUM).
2004 (English)In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, 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.
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URN: urn:nbn:se:umu:diva-100248OAI: diva2:790952
Available from: 2015-02-26 Created: 2015-02-26 Last updated: 2015-02-26

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