2001/06/04 by D. Sornette, Didier Sornette, K. Ide +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions #cond-mat.stat-mech
paper · pdf · doi:10.1142/s0129183103004462
published as Int. J. Mod. Phys. C 14 (3), 267-275 (2002) · Latex document of 14 pages including 3 eps figures
arxiv created 2001/06/04 · openalex publication_date 2003/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.