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Theory Of Self-Similar Oscillatory Finite-Time Singularities

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  • D. SORNETTE

    (Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095-1567, USA;
    Department of Earth and Space Sciences, UCLA, USA;
    Laboratoire de Physique de la Matière Condensée, CNRS UMR 6622, Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice, France)

  • K. IDE

    (Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095-1567, USA;
    Department of Atmospheric Sciences, UCLA, USA)

Abstract

A simple two-dimensional system is introduced which suggests a qualitative dynamical relationship between (1) stock market prices in the presence of nonlinear trend-followers and nonlinear value investors, (2) the world human population with a competition between a population-dependent growth rate and a nonlinear dependence on a finite carrying capacity and (3) the failure of materials subjected to a time-varying stress with a competition between positive geometrical feedback on the damage variable and nonlinear healing. Our model keeps three key ingredients (inertia, nonlinear positive and negative feedbacks) that compete to give rise to singularities in finite time decorated by accelerating oscillations.

Suggested Citation

  • D. Sornette & K. Ide, 2003. "Theory Of Self-Similar Oscillatory Finite-Time Singularities," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 267-275.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:03:n:s0129183103004462
    DOI: 10.1142/S0129183103004462
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    References listed on IDEAS

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    1. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    Cited by:

    1. Zhou, Wei-Xing & Sornette, Didier, 2009. "A case study of speculative financial bubbles in the South African stock market 2003–2006," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 869-880.
    2. Zhou, Wei-Xing & Sornette, Didier, 2003. "Evidence of a worldwide stock market log-periodic anti-bubble since mid-2000," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 543-583.
    3. Zhou, Wei-Xing & Sornette, Didier, 2003. "Renormalization group analysis of the 2000–2002 anti-bubble in the US S&P500 index: explanation of the hierarchy of five crashes and prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 584-604.
    4. Sornette, D & Takayasu, H & Zhou, W.-X, 2003. "Finite-time singularity signature of hyperinflation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(3), pages 492-506.
    5. Melecký, Jan & Sergyeyev, Artur, 2008. "A simple finite-difference stock market model involving intrinsic value," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 769-777.
    6. Didier Sornette & Wei-Xing Zhou, 2003. "The US 2000-2002 market descent: clarification," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 39-41.
    7. Westerhoff, Frank H., 2004. "Greed, fear and stock market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 635-642.

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