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Another Case of Degenerated Discrete Chenciner Dynamic System and Economics

Author

Listed:
  • Sorin Lugojan

    (Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania)

  • Loredana Ciurdariu

    (Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania)

  • Eugenia Grecu

    (Department of Management, Politehnica University of Timisoara, 300006 Timisoara, Romania)

Abstract

The non-degenerate Chenciner bifurcation of a discrete dynamical system is studied using a transformation of parameters which must be regular at the origin of the parameters (the condition CH.1 of the well-known treatise of Kuznetsov). The article studies a complementary case, where the transformation is no longer regular at the origin, representing a degeneration. Four different bifurcation diagrams appear in that degenerated case, compared to only two in the non-degenerated one. Degeneracy may cause volatility in economics systems modeled by discrete Chenciner dynamical systems.

Suggested Citation

  • Sorin Lugojan & Loredana Ciurdariu & Eugenia Grecu, 2022. "Another Case of Degenerated Discrete Chenciner Dynamic System and Economics," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3782-:d:941584
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    References listed on IDEAS

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    1. Gaunersdorfer, Andrea & Hommes, Cars H. & Wagener, Florian O.O., 2008. "Bifurcation routes to volatility clustering under evolutionary learning," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 27-47, July.
    2. Sorin Lugojan & Loredana Ciurdariu & Eugenia Grecu, 2022. "Chenciner Bifurcation Presenting a Further Degree of Degeneration," Mathematics, MDPI, vol. 10(9), pages 1-17, May.
    3. Maria Filomena Barros & Fernando Ortega, 2019. "An optimal equilibrium for a reformulated Samuelson economic discrete time system," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-10, December.
    4. Xiaoxue Li & Xiaorong Hou & Jing Yang & Min Luo, 2022. "Stability and Stabilization of 2D Linear Discrete Systems with Fractional Orders Based on the Discrimination System of Polynomials," Mathematics, MDPI, vol. 10(11), pages 1-14, May.
    5. Alidousti, J. & Eskandari, Z. & Avazzadeh, Z., 2020. "Generic and symmetric bifurcations analysis of a three dimensional economic model," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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