Improved Assessment of Orbital Stability of Rhythmic Motion with Noise
Author(s)Ahn, Jooeun; Hogan, Neville
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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.
DepartmentMassachusetts Institute of Technology. Department of Brain and Cognitive Sciences; Massachusetts Institute of Technology. Department of Mechanical Engineering
Public Library of Science
Ahn, Jooeun, and Neville Hogan. “Improved Assessment of Orbital Stability of Rhythmic Motion with Noise.” Edited by Ramesh Balasubramaniam. PLOS ONE 10, no. 3 (March 23, 2015): e0119596.
Final published version