Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-06-04
Physica A 307 (1-2), 63-106 (2002)
Physics
Condensed Matter
Statistical Mechanics
Latex document of 59 pages including 20 eps figures
Scientific paper
10.1016/S0378-4371(01)00585-4
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.
Ide K. D.
Sornette Didier
No associations
LandOfFree
Oscillatory Finite-Time Singularities in Finance, Population and Rupture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Oscillatory Finite-Time Singularities in Finance, Population and Rupture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Oscillatory Finite-Time Singularities in Finance, Population and Rupture will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-114783