Oscillatory finite-time singularities in finance, population and rupture
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In this paper, a simple two-dimensional dynamical system where two nonlinear terms, exerting respectively positive feedback and reversal, compete to create a singularity in finite time decorated by accelerating oscillations is presented.Abstract:
We present a simple two-dimensional dynamical system where two nonlinear terms, exerting respectively positive feedback and reversal, compete to create a singularity in finite time decorated by accelerating oscillations. The power law singularity results from the increasing growth rate. The oscillations result from the restoring mechanism. As a function of the order of the nonlinearity of the growth rate and of the restoring term, a rich variety of behavior is documented analytically and numerically. The dynamical behavior is traced back fundamentally to the self-similar spiral structure of trajectories in phase space unfolding around an unstable spiral point at the origin. The interplay between the restoring mechanism and the nonlinear growth rate leads to approximately log-periodic oscillations with remarkable scaling properties. Three domains of applications are discussed: (1) the stock market with a competition between 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; (3) the failure of a material subjected to a time-varying stress with a competition between positive geometrical feedback on the damage variable and nonlinear healing.read more
Citations
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Critical market crashes
Didier Sornette,Didier Sornette +1 more
TL;DR: In this paper, the authors present a general theory of financial crashes and stock market instabilities that his co-workers and the author have developed over the past seven years, and demonstrate several detailed mathematical models of speculative bubbles and crashes.
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Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth
TL;DR: It is proposed that catastrophic events are “outliers” with statistically different properties than the rest of the population and result from mechanisms involving amplifying critical cascades, and a unifying approach for modeling and predicting these catastrophic events or “ruptures,” that is, sudden transitions from a quiescent state to a crisis.
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The 2006–2008 oil bubble: Evidence of speculation, and prediction
TL;DR: In this article, the authors present an analysis of oil prices in USD and in other major currencies that diagnoses unsustainable faster-than-exponential behavior and supports the hypothesis that the recent oil price run-up was amplified by speculative behavior of the type found during a bubble-like expansion.
Journal ArticleDOI
Bubble Diagnosis and Prediction of the 2005-2007 and 2008-2009 Chinese Stock Market Bubbles
Zhi-Qiang Jiang,Wei-Xing Zhou,Didier Sornette,Didier Sornette,Ryan Woodard,Ken Bastiaensen,Peter Cauwels +6 more
TL;DR: In this paper, the authors used the logperiodic power law (LPPL) model to analyze two bubbles and subsequent market crashes in two important indexes in Chinese stock markets between May 2005 and July 2009.
Journal ArticleDOI
Bubble diagnosis and prediction of the 2005–2007 and 2008–2009 Chinese stock market bubbles
Zhi-Qiang Jiang,Wei-Xing Zhou,Didier Sornette,Didier Sornette,Ryan Woodard,Ken Bastiaensen,Peter Cauwels +6 more
TL;DR: Lin et al. as discussed by the authors used the log-periodic power law (LPPL) model to analyze two bubbles and subsequent market crashes in two important indexes in Chinese stock markets between May 2005 and July 2009.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Book
Advanced mathematical methods for scientists and engineers
Carl M. Bender,Steven A. Orszag +1 more
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
Journal ArticleDOI
Scaling and criticality in a stochastic multi-agent model of a financial market
Thomas Lux,Michele Marchesi +1 more
TL;DR: In this paper, the authors describe a multi-agent model of financial markets which supports the idea that scaling arises from mutual interactions of participants, and they find that it generates such behaviour as a result of interactions between agents.