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Complex dynamics associated with the appearance/disappearance of invariant closed curves

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  • Foroni, Ilaria
  • Agliari, Anna

Abstract

In this paper we study some global bifurcations arising in a heterogeneous financial model with fundamentalists and imitators. Such bifurcations which cause the appearance and disappearance of closed invariant curves (attracting or repelling) involve the stable and unstable sets of a saddle cycle with consequent changes in their dynamic behavior. Numerical investigations show that the transition between two qualitatively different regimes are characterized by the occurrence of homoclinic tangles with chaotic dynamics.

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  • Foroni, Ilaria & Agliari, Anna, 2011. "Complex dynamics associated with the appearance/disappearance of invariant closed curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1640-1655.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:8:p:1640-1655
    DOI: 10.1016/j.matcom.2010.12.008
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    Cited by:

    1. Anna Agliari & Pasquale Commendatore & Ilaria Foroni & Ingrid Kubin, 2014. "Expectations and industry location: a discrete time dynamical analysis," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(1), pages 3-26, April.
    2. Alina Szuz & Anna Agliari & Tonu Puu, 2015. "A Cournot triopoly with two identical producers," Gecomplexity Discussion Paper Series 13, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Aug 2015.
    3. Agliari, Anna & Pecora, Nicolò & Szuz, Alina, 2022. "Appearance of closed invariant curves in a piecewise Cournot model with advertising," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Agliari, Anna & Rillosi, Francesco & Vachadze, George, 2015. "Credit market imperfection, financial market globalization, and catastrophic transition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 41-62.

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