Principal axes for stochastic dynamics

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.

10 pages, 7 figures

References in corpus (4)

• On the proper reconstruction of complex dynamical systems spoilt by strong measurement noise
• Finite sampling interval effects in Kramers-Moyal analysis
• Extracting strong measurement noise from stochastic series: applications to empirical data
• Exact corrections for finite-time drift and diffusion coefficients

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