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On the Identification of Chaos From Frequency Content

[+] Author Affiliations
Richard Wiebe, Lawrence N. Virgin

Duke University, Durham, NC

Paper No. DETC2011-47473, pp. 823-828; 6 pages
doi:10.1115/DETC2011-47473
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5481-5
  • Copyright © 2011 by ASME

abstract

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 bounded motion) 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
Topics: Chaos

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