THEORY OF SELF-SIMILAR OSCILLATORY FINITE-TIME SINGULARITIES

D. Sornette () and K. Ide ()
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D. Sornette: Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095-1567, USA;
K. Ide: Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095-1567, USA;

International Journal of Modern Physics C (IJMPC), 2003, vol. 14, issue 03, 267-275

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.

Keywords: Singularities; population; financial crash; materials rupture; log-periodicity; self-similarity; dynamical systems; spirals (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (7)

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DOI: 10.1142/S0129183103004462

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