Date: Friday, April 06, 2018
Location: 1084 East Hall (4:10 PM to 5:00 PM)
Title: Oscillators, Asymptotic Phase, and Reduction of Dynamical Systems
Abstract: What do circadian rhythms, robot locomotion, and spiking neurons have in common? Each can be modeled by an "oscillator," or a dynamical system having a stable and periodic limiting behavior. Oscillators are usually associated with the existence of an "asymptotic phase" which governs the longterm dynamics of the oscillator and affords dimensionality reduction. Asymptotic phase has applications in diverse areas such as chemical kinetics, neuroscience, and animal locomotion.
In this talk, I will give an introduction to oscillators, asymptotic phase, and the requisite dynamical systems theory. I will also explain how asymptotic phase relates to the "Phase Response Curves" used in neuroscience. I will place the theory in the context of current research in which we develop a new algorithm to compute the asymptotic phase of an unknown oscillator, using short and noisy time series measurements. Our algorithm utilizes basic topological insights in conjunction with machine learning methods and has substantial advantages over existing techniques which require knowledge of the equations of motion, long time series, or some combination thereof.
Finally, I will show that oscillators and asymptotic phase are just one piece in a larger picture of invariant manifolds and invariant foliations and I will explain why these objects are useful for model reduction.
Files:
Speaker: Matthew Kvalheim
Institution: University of Michigan
Event Organizer: Audra McMillan amcm@umich.edu
