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On the identification of chaos from frequency content

Publication ,  Journal Article
Wiebe, R; Virgin, LN
Published in: Proceedings of the ASME Design Engineering Technical Conference
December 1, 2011

The characterization of chaos as a random-like response from a deterministic dynamical system with an extreme sensitivity to initial conditions is well-established, and has provided a stimulus to research in nonlinear dynamical systems in general. In a formal sense, the computation of the Lyapunov Exponent spectrum establishes a quantitative measure, with at least one positive Lyapunov Exponent (and generally boundedmotion) indicating a local exponential divergence of adjacent trajectories. However, although the extraction of Lyapunov Exponents can be accomplished with (necessarily noisy) experimental data, this is still a relatively data-intensive and sensitive endeavor. We present here an alternative, pragmatic approach to identifying chaos as a function of system parameters using response frequency characteristics and extending the concept of the spectrogram. Copyright © 2011 by ASME.

Duke Scholars

Published In

Proceedings of the ASME Design Engineering Technical Conference

DOI

Publication Date

December 1, 2011

Volume

4

Issue

PARTS A AND B

Start / End Page

823 / 828
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Wiebe, R., & Virgin, L. N. (2011). On the identification of chaos from frequency content. Proceedings of the ASME Design Engineering Technical Conference, 4(PARTS A AND B), 823–828. https://doi.org/10.1115/DETC2011-47473
Wiebe, R., and L. N. Virgin. “On the identification of chaos from frequency content.” Proceedings of the ASME Design Engineering Technical Conference 4, no. PARTS A AND B (December 1, 2011): 823–28. https://doi.org/10.1115/DETC2011-47473.
Wiebe R, Virgin LN. On the identification of chaos from frequency content. Proceedings of the ASME Design Engineering Technical Conference. 2011 Dec 1;4(PARTS A AND B):823–8.
Wiebe, R., and L. N. Virgin. “On the identification of chaos from frequency content.” Proceedings of the ASME Design Engineering Technical Conference, vol. 4, no. PARTS A AND B, Dec. 2011, pp. 823–28. Scopus, doi:10.1115/DETC2011-47473.
Wiebe R, Virgin LN. On the identification of chaos from frequency content. Proceedings of the ASME Design Engineering Technical Conference. 2011 Dec 1;4(PARTS A AND B):823–828.

Published In

Proceedings of the ASME Design Engineering Technical Conference

DOI

Publication Date

December 1, 2011

Volume

4

Issue

PARTS A AND B

Start / End Page

823 / 828