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Some global bifurcations related to the appearance of closed invariant curves

Anna Agliari (), Laura Gardini () 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)
Date: 2005
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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

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