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Theory of self-similar oscillatory finite-time singularities in Finance, Population and Rupture

D. Sornette·K. Ide
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Abstract

This is a short letter summarizing the long paper cond-mat/0106047 in which we present a simple two-dimensional dynamical system reaching a singularity in finite time decorated by accelerating oscillations due to the interplay between nonlinear positive feedback and reversal in the inertia. This provides a fundamental equation for the dynamics of (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 a material subject to a time-varying stress with a competition between positive geometrical feedback on the damage variable and nonlinear healing. The rich fractal scaling properties of the dynamics are traced back to the self-similar spiral structure in phase space unfolding around an unstable spiral point at the origin.

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BibTeXRIS

D. Sornette, K. Ide. 2001-06-04. Theory of self-similar oscillatory finite-time singularities in Finance, Population and Rupture. https://doi.org/10.1142/s0129183103004462

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