On the identification of chaos from frequency content

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Wiebe, R; Virgin, LN

Published Date

  • December 1, 2011

Published In

  • Proceedings of the Asme Design Engineering Technical Conference

Volume / Issue

  • 4 / PARTS A AND B

Start / End Page

  • 823 - 828

Digital Object Identifier (DOI)

  • 10.1115/DETC2011-47473

Citation Source

  • Scopus