From Data to Dynamics: Periodic Orbits

J. Guckenheimer (Math, Cornell)

The physical sciences derive "first prinicples" models for many phenomena and then try to fit these models to observational data. Fitting procedures need further development when the data come from time series measurements of dynamical behavior. Systems that lack good models are even more problematic. This talk will discuss "data driven" models of motion capture data of cockroach and human running. Floquet theory is used formulate simple models for the dynamics near a stable periodic orbit, and these are fit to the data taking into account stochastic fluctuations. The analysis leads us to pose mathematical questions about how much data is required to produce accurate estimates for the parameters of a stochastic system.