Parameter estimation, nonlinearity and Occam's razor

TL;DR

This paper introduces a method to identify nonlinear systems driven by simple forces using a discrete transformation based on synchronization, demonstrated with birdsong respiratory data.

Contribution

It develops a novel parameter estimation technique that detects nonlinearity and minimal complexity in driving forces from time series data.

Findings

Successfully applied to birdsong respiratory patterns

Effective in distinguishing nonlinear responses from simple forcing

Provides a new tool for analyzing complex biological signals

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.