Browsing by Author "Bollt, Erik M."

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    Collective behaviour across animal species
    DeLellis, P.; Polverino, G.; Ustuner, G.; Abaid, Nicole; Macri, S.; Bollt, Erik M.; Porfiri, M. (Nature Publishing Group, 2014-01-01)
    We posit a new geometric perspective to define, detect, and classify inherent patterns of collective behaviour across a variety of animal species. We show that machine learning techniques, and specifically the isometric mapping algorithm, allow the identification and interpretation of different types of collective behaviour in five social animal species. These results offer a first glimpse at the transformative potential of machine learning for ethology, similar to its impact on robotics, where it enabled robots to recognize objects and navigate the environment.
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    Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?
    Bollt, Erik M.; Ross, Shane D. (MDPI, 2021-10-28)
    This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field is a Koopman eigenfunction. Restricting ourselves to polynomial vector fields to make this construction easier, we find that such vector fields do exist, and we explore whether such vector fields have a special structure, thus making a link between the geometric theory and the transfer operator theory.