Parameter estimation, nonlinearity and Occam's razor
Quantitative Methods
2015-06-01 v1 Chaotic Dynamics
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.
Cite
@article{arxiv.1410.8230,
title = {Parameter estimation, nonlinearity and Occam's razor},
author = {Leandro M. Alonso},
journal= {arXiv preprint arXiv:1410.8230},
year = {2015}
}