Improving empirical characteristic multiplier estimation through a change of basis
© 2020 This paper applies empirical Floquet theory to extract characteristic multipliers from time series data and builds upon prior works by significantly reducing the influence of experimental noise. Characteristic multipliers (CMs), which are the eigenvalues of the transition matrix governing the evolution of transient solutions over one period of motion, quantify the local stability of periodic orbits and can be estimated experimentally without knowledge of the system model. Traditionally, empirical CM estimates were obtained from the transient dynamics observed by subtracting measured steady-state behavior from a recorded perturbed response. The subtraction of two experimentally measured quantities amplifies noise, producing inaccurate CM estimates. By applying a moving integral to isolate the transient dynamics, this work provides an approach to reduce, rather than amplify, the influence of noise on empirical CM results. This approach is applied to the reconstructed phase space of a numerical example and an experimental system to demonstrate the improvements.
Little, JA; Turner, JD; Mann, BP
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