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  • eBook:Analysis of Chaotic Behavior in Non-linear Dynamical Systems

    Analysis of Chaotic Behavior in Non-linear Dynamical Systems

    Models and Algorithms for Quaternions
    Michał Piórek
    978-3-319-94887-4
    2019
    Edition 1
    • Introduces the first analysis of chaos in the processes described by quaternions
    • Provides an analysis of chaotic behavior in non-linear dynamical systems using models and algorithms of quaternions
    • Includes methods that allow not only the detection of deterministic chaos in quaternion time series but also the classification of the nature of the dynamical system, which drives the quaternion time series
    • Proposes methodology to identify three types of the quaternion time series: random, periodic, and chaotic
    • Brings additional value by proposing a framework of quaternion clustering, which includes the proposition of a quaternions clustering algorithm along with the measures of the quaternions clustering validity
    • Tests the quality of quaternion clustering against three parameters of the input data set: real clusters number, overlapping degree, and variance of the data set
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