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Theory of self-similar oscillatory finite-time singularities in Finance, Population and Rupture | | D. Sornette
; K. Ide
; | | Date: |
4 Jun 2001 | | Journal: | Int. J. Mod. Phys. C 14 (3), 267-275 (2002) | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | Univ. Nice/CNRS and UCLA) and K. Ide (UCLA | | 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. | | Source: | arXiv, cond-mat/0106054 | | Services: | Forum | Review | PDF | Favorites | |
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