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Some global bifurcations related to the appearance of closed invariant curves
Catholic University, Dipartimento di Scienze Economiche e Sociali, Piacenza, Italy.
Dept. Scienze Economiche, University of Urbino, Italy.
Umeå University, Faculty of Social Sciences, Centre for Regional Science (CERUM).
2005 (English)In: Mathematics and Computers in Simulation, ISSN 0378-4754, Vol. 68, no 3, 201-219 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider a two-dimensional map (a duopoly game) in which the fixed point is destabilized via a subcritical Neimark–Hopf (N–H) bifurcation. Our aim is to investigate, via numerical examples, some global bifurcations associated with the appearance of repelling closed invariant curves involved in the Neimark–Hopf bifurcations. We shall see that the mechanism is not unique, and that it may be related to homoclinic connections of a saddle cycle, that is to a closed invariant curve formed by the merging of a branch of the stable set of the saddle with a branch of the unstable set of the same saddle. This will be shown by analyzing the bifurcations arising inside a periodicity tongue, i.e., a region of the parameter space in which an attracting cycle exists.

Place, publisher, year, edition, pages
2005. Vol. 68, no 3, 201-219 p.
Keyword [en]
Discrete dynamical systems, Duopoly models, Subcritical Neimark–Hopf bifurcation, Homoclinic connection
National Category
URN: urn:nbn:se:umu:diva-100246OAI: diva2:790958
Available from: 2015-02-26 Created: 2015-02-26 Last updated: 2015-02-26

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