Skip to main content
Journal cover image

Parameter estimation for chaotic systems using a geometric approach: Theory and experiment

Publication ,  Journal Article
Olson, CC; Nichols, JM; Virgin, LN
Published in: Nonlinear Dynamics
October 1, 2012

A method for estimating model parameters based on chaotic system response data is described. This estimation problem is made challenging by sensitive dependence to initial conditions. The standard maximum likelihood estimation method is practically infeasible due to the non-smooth nature of the likelihood function. We bypass the problem by introducing an alternative, smoother function that admits a better-defined maximum and show that the parameters that maximize this new function are asymptotically equivalent to maximum likelihood estimates. We use simulations to explore the influence of noise and available data on model Duffing and Lorenz oscillators. We then apply the approach to experimental data from a chaotic Duffing system. Our method does not require estimation of initial conditions and parameter estimates may be obtained even when system dynamics have been estimated from a delay embedding. © 2012 Springer Science+Business Media B.V.

Duke Scholars

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

October 1, 2012

Volume

70

Issue

1

Start / End Page

381 / 391

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Olson, C. C., Nichols, J. M., & Virgin, L. N. (2012). Parameter estimation for chaotic systems using a geometric approach: Theory and experiment. Nonlinear Dynamics, 70(1), 381–391. https://doi.org/10.1007/s11071-012-0461-8
Olson, C. C., J. M. Nichols, and L. N. Virgin. “Parameter estimation for chaotic systems using a geometric approach: Theory and experiment.” Nonlinear Dynamics 70, no. 1 (October 1, 2012): 381–91. https://doi.org/10.1007/s11071-012-0461-8.
Olson CC, Nichols JM, Virgin LN. Parameter estimation for chaotic systems using a geometric approach: Theory and experiment. Nonlinear Dynamics. 2012 Oct 1;70(1):381–91.
Olson, C. C., et al. “Parameter estimation for chaotic systems using a geometric approach: Theory and experiment.” Nonlinear Dynamics, vol. 70, no. 1, Oct. 2012, pp. 381–91. Scopus, doi:10.1007/s11071-012-0461-8.
Olson CC, Nichols JM, Virgin LN. Parameter estimation for chaotic systems using a geometric approach: Theory and experiment. Nonlinear Dynamics. 2012 Oct 1;70(1):381–391.
Journal cover image

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

October 1, 2012

Volume

70

Issue

1

Start / End Page

381 / 391

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences