Handbook of Applications of Chaos Theory (Hardback) book cover

Handbook of Applications of Chaos Theory

Edited by Christos H. Skiadas, Charilaos Skiadas

© 2016 – Chapman and Hall/CRC

934 pages | 612 B/W Illus.

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Hardback: 9781466590434
pub: 2016-06-01
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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

Index

About the Editors

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.

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT004000
MATHEMATICS / Arithmetic
MAT007000
MATHEMATICS / Differential Equations