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Related Experiment Video

Updated: May 27, 2026

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Principal axes for stochastic dynamics.

V V Vasconcelos¹, F Raischel, M Haase

¹Physics Department, Faculty of Sciences, University of Lisbon, P-1649-003 Lisbon, Portugal.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 9, 2011

Summary

This summary is machine-generated.

We present a new method to determine the number of independent stochastic sources in complex systems. This approach uses eigenvalues and eigenvectors of diffusion matrices to enhance system predictability.

Related Experiment Videos

Last Updated: May 27, 2026

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Area of Science:

Complex Systems Dynamics
Stochastic Processes
Nonlinear Dynamics

Background:

Complex systems are often modeled using coupled Langevin equations.
Understanding the number of independent stochastic sources is crucial for accurate modeling.
Existing methods may be limited in scope or applicability.

Purpose of the Study:

To introduce a general procedure for directly ascertaining the number of independent stochastic sources.
To provide a method applicable to coupled Langevin equations of arbitrary dimension.
To enhance the predictability of complex systems.

Main Methods:

Computation of eigenvalues and eigenvectors of local diffusion matrices.
Application of the algorithm to systems exhibiting Hopf bifurcation.
Definition of vector fields of stochastic eigendirections using eigenvectors.

Main Results:

The procedure successfully determines the number of independent stochastic sources.
The eigenvector associated with the lowest eigenvalue identifies the path of minimum stochastic forcing.
Transformation to an eigenvector-aligned coordinate system improves system predictability.

Conclusions:

The developed procedure offers a direct and general method for source identification.
The analysis of diffusion matrix eigenvectors provides insights into system dynamics.
This approach has implications for controlling and predicting the behavior of complex stochastic systems.