Nonlinear Dynamics

, Volume 79, Issue 2, pp 1207–1216 | Cite as

New invariant measures to track slow parameter drifts in fast dynamical systems

  • Son Hai Nguyen
  • David Chelidze
Original Paper


Estimates of quantitative characteristics of nonlinear dynamics, e.g., correlation dimension or Lyapunov exponents, require long time series and are sensitive to noise. Other measures (e.g., phase space warping or sensitivity vector fields) are relatively difficult to implement and computationally intensive. In this paper, we propose a new class of features based on Birkhoff ergodic theorem, which are fast and easy to calculate. They are robust to noise and do not require large data or computational resources. Application of these metrics in conjunction with the smooth orthogonal decomposition to identify/track slowly changing parameters in nonlinear dynamical systems is demonstrated using both synthetic and experimental data.


Dynamical systems Invariant measures Characteristic distance Smooth orthogonal decomposition Parameter tracking 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mechanical, Industrial and Systems EngineeringUniversity of Rhode IslandKingstonUSA

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