E-Book, Englisch, 206 Seiten
Banerjee / Mukherjee / Hassan Fractals
1. Auflage 2017
ISBN: 978-1-4987-4136-1
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
Patterns in Nonlinear Dynamics and Applications
E-Book, Englisch, 206 Seiten
ISBN: 978-1-4987-4136-1
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
The aim of this book is to describe the essence of fractals and multifractals dynamics in the applications of bioscience and engineering, bioinformatics, and financial time series. To reach these aims, the book covers the basic idea, history, structure, methodology and analysis of fractals, the relationship between fractals and nonlinear dynamics, the applications of fractal and multifractal analysis in biomedical science, and how fractal signals and images are modelled by Iterated Function system. Illustrations and practical applications are given throughout the text to provide clear interpretations and explanations of various complex fractal objects and fractal modelling.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Fractal – A Non-Differentiable Geometry. Evolution of fractal – a basic introduction. Classification of fractal – a brief review. Deterministic fractal. Random fractal. Note on Connectivity properties. Bibliography. Complex World in View of Nonlinear Dynamics. What is the meaning of complex world?Why nonlinear dynamics is still significant? Describing complex phenomena. Meaning of nonlinear dynamics – Physical and mathematical perception. Heuristic approach of nonlinear dynamics in site of mathematical knowledge. Connection between fractal and nonlinear dynamics. Bibliography. Measure of Roughness for Deterministic System. Topological dimension. Point wise dimension. Correlation dimension. Generalized correlation dimension – Multifractal analysis. Bibliography. Measure of Roughness for stochastic system. Stationary time series and Non-stationary time series. Fluctuation analysis. Hurst Exponent. Detrended Fluctuation Analysis. Generalized Hurst Exponent. Multifractal Detrended Fluctuation Analysis. Bibliography. Application in Biomedical Signal. ECG signal and its Fractal analysis. Interpretation of dynamics of EMG signal. Fractals and multifractal analysis of EEG signal. Multifractal analysis of HRV. Bibliography. Application in Bioinformatics and Finance. Method of signal analysis in term of DNA sequence. Discussion on Financial time series in view of stochastic time series. Analysis of fractal and multifractal landscape of DNA sequence. Application of fractal and multifractal analysis in financial time series. Bibliography. Metric Space and Space of Fractals. Basic concept of metric space. Review of complete and compact metric space. Connection between fractals and metric space. Review on contraction mapping and fixed point theorem. Bibliography. Application of Fractal in Image Signal. Introduction: Chaos game. Iterated functions systems. Fractal Interpolation. Modelling signal and image by IFS. Bibliography.
