Analysis of Chaotic Behavior in Non-linear Dynamical Systems

Description

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. Front Matter ....Pages i-xi Introduction (Michał Piórek)....Pages 1-5 Processes Described by Quaternion Models (Michał Piórek)....Pages 7-17 Deterministic Chaos Properties (Michał Piórek)....Pages 19-34 Analysis of Chaos from Time Series - Existing Methods Survey (Michał Piórek)....Pages 35-43 Analysis of Chaos from Quaternion Time Series - Proposed Methods (Michał Piórek)....Pages 45-64 Numerical Experiments (Michał Piórek)....Pages 65-71 Analysis of Chaos for Quaternion Time Series (Michał Piórek)....Pages 73-88 Comparison Against Existing Approaches (Michał Piórek)....Pages 89-110 Quaternions Clustering (Michał Piórek)....Pages 111-121 Summary (Michał Piórek)....Pages 123-125 Back Matter ....Pages 127-132