Exploration of Order in Chaos with Replica Exchange Monte Carlo
Statistical Mechanics
2009-11-13 v2 Chaotic Dynamics
Abstract
A method for exploring unstable structures generated by nonlinear dynamical systems is introduced. It is based on the sampling of initial conditions and parameters by Replica Exchange Monte Carlo (REM), and efficient both for the search of rare initial conditions and for the combined search of rare initial conditions and parameters. Examples discussed here include the sampling of unstable periodic orbits in chaos and search for the stable manifold of unstable fixed points, as well as construction of the global bifurcation diagram of a map.
Keywords
Cite
@article{arxiv.0811.2944,
title = {Exploration of Order in Chaos with Replica Exchange Monte Carlo},
author = {Tatsuo Yanagita and Yukito Iba},
journal= {arXiv preprint arXiv:0811.2944},
year = {2009}
}
Comments
Read at SigmaPhi2008. Submitted to J. Stat. Mech