CNCS Center for Nonlinear and Complex Systems
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Publications [#282404] of Lawrence N. Virgin

Papers Published

  1. Wiebe, R; Virgin, LN, On the identification of chaos from frequency content, Proceedings of the Asme Design Engineering Technical Conference, vol. 4 no. PARTS A AND B (December, 2011), pp. 823-828 [doi]
    (last updated on 2019/09/16)

    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.