title: Improved assessment of orbital stability of rhythmic motion with noise.
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.
authors: Department of Mechanical Engineering, University of Victoria, Victoria, British Colombia, Canada.
authors: Jooeun
authors: J
authors: Ahn
authors: Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America; Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America.
authors: Neville
authors: N
authors: Hogan
mesh_terms: D001696:Biomechanical Phenomena; D005684:Gait / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D009038:Motion; D009622:Noise; D010507:Periodicity; D016138:Walking