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arXiv · 1410.8230

Parameter estimation, nonlinearity and Occam's razor

Leandro M. Alonso
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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.

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Leandro M. Alonso. 2014-10-30. Parameter estimation, nonlinearity and Occam's razor. https://doi.org/10.1063/1.4914452

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