Characterization of Dolphin Acoustic Echo-Location Data using a Dynamical Classification Method

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Abstract
Many methods for time series analysis derived from nonlinear dynamical systems theory have been developed in the last decade, and have demonstrated remarkable results in a variety of simulated, experimental, and real applications. Classification of time series based on the underlying dynamical generator is also potentially powerful, and we have previously presented a method for dynamical classification based on empirically estimated sets of nonlinear ordinary differential equations, i.e. global dynamical models. A particularly useful area of application for such methods may be biologic and medical data analysis, where few quantitative methods exist for the highly complex time evolutions. Here, as an example of the application of such classification methods, we present an analysis of data of the acoustic pulse trains produced by dolphins as they attempt to echo-locate objects in an ocean environment, which is derived from a controlled experimental framework.