title: Parameter estimation, nonlinearity, and Occam's razor.
abstract: Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple harmonic function. In order to identify if a recorded time series is the result of a nonlinear system responding to a simpler forcing, we develop a discrete nonlinear transformation for time series based on synchronization techniques. This allows a parameter estimation procedure which simultaneously searches for a good fit of the recorded data, and small complexity of a fluctuating driving parameter. We illustrate this procedure using data from respiratory patterns during birdsong production.
authors.affiliation: Laboratory of Mathematical Physics, Center for Studies in Physics and Biology, The Rockefeller University, New York, New York 10065, USA.
authors.forename: Leandro M
authors.initials: LM
authors.lastname: Alonso