Title: Phase-Amplitude-Based Techniques for Control and Analysis of Strongly Perturbed Limit Cycle Oscillators

Speaker: Dan Wilson, University of Tennessee, Knoxville

Abstract: While phase-based reduction techniques have a rich history in the analysis and control of oscillatory dynamical systems, the overwhelming majority of theoretical analysis in this field has been performed in the weakly perturbed limit. Comparatively very little is understood about limit cycle oscillators in response to strong and/or long-lasting perturbations, mostly due to the lack of viable reduction strategies that are valid when considering strong perturbations. In this presentation, I will discuss the use of isostable coordinates, which characterize level sets of the slowest decaying eigenmodes of the Koopman operator in conjunction with phase-based techniques to yield analytically tractable reduced order models that are valid in the strongly perturbed regime. Applications involving phase resetting of circadian rhythms following rapid travel across multiple time zones illustrate the utility of these new methods in situations where standard, phase-only techniques fail. I will also discuss related work motivated by experimental and detailed computational studies finding that coupled circadian oscillators with decreased levels of synchronization are able to more rapidly adjust to changes in circadian time. Theoretical analysis reveals the dynamics of mean-field coupled oscillators can be considered in the context of a supercritical Hopf bifurcation, ultimately providing an explanation for the fundamental relationship between synchronization and phase resetting efficiency. In the context of jet-lag recovery strategies, further analysis reveals that transient desynchronization facilitates phase resetting when the relaxation rate of the population limit cycle is sufficiently slow relative to the natural frequency of the population oscillation.

Zoom: https://northwestern.zoom.us/j/91324444590

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