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On the global dynamics of a finance model

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  • Llibre, Jaume
  • Valls, Clàudia

Abstract

Recently several works have studied the following model of finance x˙=z+(y−a)x,y˙=1−by−x2,z˙=−x−cz,where a, b and c are positive real parameters. We study the global dynamics of this polynomial differential system, and in particular for a one–dimensional parametric subfamily we show that there is an equilibrium point which is a global attractor.

Suggested Citation

  • Llibre, Jaume & Valls, Clàudia, 2018. "On the global dynamics of a finance model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 1-4.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:1-4
    DOI: 10.1016/j.chaos.2017.10.026
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    References listed on IDEAS

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    1. Škovránek, Tomáš & Podlubny, Igor & Petráš, Ivo, 2012. "Modeling of the national economies in state-space: A fractional calculus approach," Economic Modelling, Elsevier, vol. 29(4), pages 1322-1327.
    2. Arikoglu, Aytac & Ozkol, Ibrahim, 2009. "Solution of fractional integro-differential equations by using fractional differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 521-529.
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    Cited by:

    1. Alexeeva, Tatyana A. & Barnett, William A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2020. "Dynamics of the Shapovalov mid-size firm model," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Xu, Fei & Lai, Yongzeng & Shu, Xiao-Bao, 2018. "Chaos in integer order and fractional order financial systems and their synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 125-136.
    3. Veronika NOVOTNA & Stanislav Å KAPA & Bernard NEUWIRTH, 2019. "Analysis Of A Non-Linear Dynamic Financial System," Proceedings of the INTERNATIONAL MANAGEMENT CONFERENCE, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 13(1), pages 288-297, November.
    4. Li, Shimin & Llibre, Jaume, 2019. "Phase portraits of continuous piecewise linear Liénard differential systems with three zones," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 149-157.

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