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Improved Assessment of Orbital Stability of Rhythmic Motion with Noise

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  • Jooeun Ahn
  • Neville Hogan

Abstract

Mathematical techniques have provided tools to quantify the stability of rhythmic movements of humans and machines as well as mathematical models. One archetypal example is the use of Floquet multipliers: assuming periodic motion to be a limit-cycle of a nonlinear oscillator, local stability has been assessed by evaluating the rate of convergence to the limit-cycle. However, the accuracy of the assessment in experiments is questionable: Floquet multipliers provide a measure of orbital stability for deterministic systems, but various components of biological systems and machines involve inevitable noise. In this study, we show that the conventional estimate of orbital stability, which depends on regression, has bias in the presence of noise. We quantify the bias, and devise a new method to estimate orbital stability more accurately. Compared with previous methods, our method substantially reduces the bias, providing acceptable estimates of orbital stability with an order-of-magnitude fewer cycles.

Suggested Citation

  • Jooeun Ahn & Neville Hogan, 2015. "Improved Assessment of Orbital Stability of Rhythmic Motion with Noise," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-12, March.
    • Handle: RePEc:plo:pone00:0119596
    DOI: 10.1371/journal.pone.0119596
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    Cited by:

    1. Siddhartha Bikram Panday & Prabhat Pathak & Jeheon Moon & Dohoon Koo, 2022. "Complexity of Running and Its Relationship with Joint Kinematics during a Prolonged Run," IJERPH, MDPI, vol. 19(15), pages 1-24, August.
    2. Namki Choi & Hwanhee Cho & Byongjun Lee, 2019. "Development of Floquet Multiplier Estimator to Determine Nonlinear Oscillatory Behavior in Power System Data Measurement," Energies, MDPI, vol. 12(10), pages 1-18, May.

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