Analysis of Chaotic Behavior in Non-linear Dynamical Systems

This book presents a new approach for the analysis of chaotic behavior in non-linear dynamical systems, in which output can be represented in quaternion parametrization. It offers a new family of methods for the analysis of chaos in the quaternion domain along with extensive numerical experiments performed on human motion data and artificial data. All methods and algorithms are designed to allow detection of deterministic chaos behavior in quaternion data representing the rotation of a body in 3D space. This book is an excellent reference for engineers, researchers, and postgraduate students conducting research on human gait analysis, healthcare informatics, dynamical systems with deterministic chaos or time series analysis.

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

Inhalt
Introduction.- Processes described by quaternion models.- Deterministic chaos properties.- Analysis of chaos from time series-existing methods survey.- Analysis of chaos from quaternion time series-proposed methods.- Numerical Experiments.- Analysis of chaos for quaternion time series.- Comparison against existing approaches.- Quaternions clustering.- Summary.<p