 Some global bifurcations related to the appearance of closed invariant curvesAnna Agliari (anna.agliari@unicatt.it), Laura Gardini (laura.gardini@uniurb.it) and Tönu Puu Mathematics and Computers in Simulation (MATCOM), 2005, vol. 68, issue 3, 201-219 Abstract: 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. Keywords: Discrete dynamical systems; Duopoly models; Subcritical Neimark–Hopf bifurcation; Homoclinic connection (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:68:y:2005:i:3:p:201-219 DOI: 10.1016/j.matcom.2004.12.003 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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