Estimating interdependences in networks of weakly coupled deterministic systems

Oscar De Feo and Cristian Carmeli
Phys. Rev. E 77, 026711 – Published 27 February 2008

Abstract

The extraction of information from measured data about the interactions taking place in a network of systems is a key topic in modern applied sciences. This topic has been traditionally addressed by considering bivariate time series, providing methods which are sometimes difficult to extend to multivariate data, the limiting factor being the computational complexity. Here, we present a computationally viable method based on black-box modeling which, while theoretically applicable only when a deterministic hypothesis about the processes behind the recordings is plausible, proves to work also when this assumption is severely affected. Conceptually, the method is very simple and is composed of three independent steps: in the first step a state-space reconstruction is performed separately on each measured signal; in the second step, a local model, i.e., a nonlinear dynamical system, is fitted separately on each (reconstructed) measured signal; afterward, a linear model of the dynamical interactions is obtained by cross-relating the (reconstructed) measured variables to the dynamics unexplained by the local models. The method is successfully validated on numerically generated data. An assessment of its sensitivity to data length and modeling and measurement noise intensity, and of its applicability to large-scale systems, is also provided.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
1 More
  • Received 15 May 2006

DOI:https://doi.org/10.1103/PhysRevE.77.026711

©2008 American Physical Society

Authors & Affiliations

Oscar De Feo*

  • Department of Microelectronic Engineering, University College Cork, North Mall, Cork, Ireland

Cristian Carmeli

  • Laboratory of Nonlinear Systems, Swiss Federal Institute of Technology Lausanne, EPFL IC LANOS, Station 14, 1015 Lausanne, Switzerland

  • *oscar.defeo@ucc.ie
  • Present address: Department of Electronics & Information Engineering, Hong Kong Polytechnic University, Hung Hom Kowloon, Hong Kong. cristian.carmeli@polyu.edu.hk

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 77, Iss. 2 — February 2008

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×