1st Edition

Handbook of Applications of Chaos Theory

ISBN 9781466590434
Published June 1, 2016 by Chapman and Hall/CRC
952 Pages 612 B/W Illustrations

USD $250.00

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Book Description

In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications.

Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs.

The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.

Table of Contents

Chaos and Nonlinear Dynamics
The Intermittency Route to Chaos
Ezequiel del Rio and Sergio Elaskar
Deterministic Chaos and Evolutionary Dynamics: Mutual Relations
Ivan Zelinka
On the Transition to Phase Synchronized Chaos
Erik Mosekilde, Jakob L. Laugesen, and Zhanybai T. Zhusubaliyev
The Kolmogorov–Taylor Law of Turbulence: What Can Rigorously Be Proved?
Roger Lewandowski
Nonlinear Dynamics of Two-Dimensional Chaos Maps and Fractal Sets for Snow Crystals
Nguyen H. Tuan Anh, Dang Van Liet, and Shunji Kawamoto
Fractional Chen Oscillators
C.M.A. Pinto and A.R.M. Carvalho

Strange Attractors, Bifurcation, and Related Theory
Strange Attractors and Classical Stability Theory: Stability, Instability, Lyapunov Exponents, and Chaos
Nikolay Kuznetsov and Gennady Leonov
Numerical Visualization of Attractors: Self-Exciting and Hidden Attractors
Nikolay Kuznetsov and Gennady Leonov
Bifurcation Analysis of a Simple 3D BVP Oscillator and Chaos Synchronization of Its Coupled Systems
Yusuke Nishiuchi and Tetsushi Ueta
Capture of a Particle into Resonance
Oleg Mikhailovich Kiselev

Chaotic Data Analysis, Equations, and Applications
Integral Equations and Applications
A.G. Ramm
Large-Time Behavior of Solutions to Evolution Equations
A.G. Ramm
Empirical Wavelet Coefficients and Denoising of Chaotic Data
in the Phase Space
Matthieu Garcin
Characterization of Time Series Data
Christopher W. Kulp and Brandon J. Niskala
Geometry of Local Instability in Hamiltonian Dynamics
M. Lewkowicz, J. Levitan, Y. Ben Zion, and L. Horwitz
Chaos Analysis of ER-Network Dynamics in Microscopy Imaging
Tuan D. Pham and Ikuo Wada
Supersymmetric Theory of Stochastics: Demystification of Self-Organized Criticality
Igor V. Ovchinnikov
New Robust Stability of Discrete-Time Hybrid Systems
Grienggrai Rajchakit

Chaos in Plasma
Chaos in Plasma Physics
Dan-Gheorghe Dimitriu and Maricel Agop
Plasma Harmonic and Overtone Coupling
Victor J. Law

Chaos in Flows and Turbulence
Wave Turbulence in Vibrating Plates
O. Cadot, M. Ducceschi, T. Humbert, B. Miquel, N.Mordant, C. Josserand, and C. Touzé
Nonlinear Dynamics of the Oceanic Flow
S.V. Prants, M.V. Budyansky, and M.Yu. Uleysky
The Suspensions of Maps to Flows
John Starrett
Lagrangian Coherent Structures at the Onset of Hyperchaos in Two-Dimensional Flows
Rodrigo A. Miranda, Erico L. Rempel, Abraham C.-L. Chian, and Adriane B. Schelin

Chaos and Quantum Theory
Chaotic Interference versus Decoherence: External Noise, State Mixing, and Quantum-Classical Correspondence
Valentin V. Sokolov and Oleg V. Zhirov
Application of Microwave Networks to Simulation of Quantum Graphs
Michał Ławniczak, Szymon Bauch, and Leszek Sirko

Optics and Chaos
Optics and Chaos: Chaotic, Rogue, and Noisy Optical Dissipative Solitons
Vladimir L. Kalashnikov
Hyperbolic Prism, Poincaré Disk, and Foams
Alberto Tufaile and Adriana Pedrosa Biscaia Tufaile
Parhelic-Like Circle and Chaotic Light Scattering
Adriana Pedrosa Biscaia Tufaile and Alberto Tufaile

Chaos Theory in Biology and Medicine
Applications of Extreme Value Theory in Dynamical Systems for the Analysis of Blood Pressure Data
Davide Faranda
Comb Models for Transport along Spiny Dendrites
V. Méndez and A. Iomin
Applications of Chaos Theory Methods in Clinical Digital Pathology
Wlodzmierz Klonowski

Chaos in Mechanical Sciences
System Augmentation for Detection and Sensing: Theory and Applications
Kiran D’Souza and Bogdan I. Epureanu
Unveiling Complexity of Church Bells Dynamics Using Experimentally Validated Hybrid Dynamical Model
Piotr Brzeski, Tomasz Kapitaniak, and Przemyslaw Perlikowski
Multiple Duffing Problems Based on Hilltop Bifurcation Theory on MFM Models
Ichiro Ario

Chaotic Pattern Recognition
The Science and Art of Chaotic Pattern Recognition
B. John Oommen, Ke Qin, and Dragos Calitoiu

Chaos in Socioeconomic and Human Sciences
Why Economics Has Not Accomplished What Physics Has?
Marisa Faggini and Anna Parziale
Human Fuzzy Rationality as a Novel Mechanism of Emergent Phenomena
Ihor Lubashevsky
Chaos in Monolingual and Bilingual Speech
Elena Babatsouli

Chaos in Music
Composers and Chaos: A Survey of Applications of Chaos Theory in Musical Arts and Research
Scott Mc Laughlin


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Christos H. Skiadas, PhD, was the founder and director of the Data Analysis and Forecasting Laboratory at the Technical University of Crete. He is chair of the Chaotic Modeling and Simulation Conference series. He has published more than 80 papers, three monographs, and 12 books, including Chaotic Modeling and Simulation: Analysis of Chaotic Models, Attractors and Forms (Chapman & Hall/CRC, October 2008). His research interests include innovation diffusion modeling and forecasting, life table data modeling, healthy life expectancy estimates, and deterministic, stochastic, and chaotic modeling.

Charilaos Skiadas, PhD, is an associate professor in mathematics and computer science at Hanover College. He is the coauthor of Chaotic Modeling and Simulation: Analysis of Chaotic Models, Attractors and Forms (Chapman & Hall/CRC, October 2008). His research interests encompass a wide array of mathematical and computing topics, ranging from algebraic geometry to statistics and programming languages to data science.