Skip to main content
Article thumbnail
Location of Repository

Principal axes for stochastic dynamics

By V. V. Vasconcelos, F. Raischel, M. Haase, J. Peinke, M. Wächter, P. G. Lind and D. Kleinhans

Abstract

We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf-bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.Comment: 10 pages, 7 figure

Topics: Physics - Data Analysis, Statistics and Probability, Physics - Computational Physics
Year: 2013
DOI identifier: 10.1103/PhysRevE.84.031103
OAI identifier: oai:arXiv.org:1105.1700
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://arxiv.org/abs/1105.1700 (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.