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.

section 1|1 pages

Chaos and Nonlinear Dynamics

chapter 1|18 pages

The Intermittency Route to Chaos

ByEzequiel del Rio, Sergio Elaskar

chapter 2|18 pages

Deterministic Chaos and Evolutionary Dynamics: Mutual Relations

ByIvan Zelinka

chapter 3|23 pages

On the Transition to Phase Synchronized Chaos

ByErik Mosekilde, Jakob Lund Laugesen, Zhanybai T. Zhusubaliyev

chapter 4|19 pages

The Kolmogorov-Taylor Law of Turbulence: What Can Rigorously Be Proved?

ByRoger Lewandowski

chapter 5|9 pages

Nonlinear Dynamics of Two-Dimensional Chaotic Maps and Fractal Sets for Snow Crystals

ByNguyen H. Tuan Anh, Dang Van Liet, Shunji Kawamoto

chapter 6|9 pages

Fractional Chen Oscillators

ByC.M.A. Pinto, Ana R.M. Carvalho

section 2|1 pages

Strange Attractors, Bifuracation, and Related Theory

chapter 8|9 pages

Numerical Visualization of Attractors: Self-Exciting and Hidden Attractors

ByNikolay Kunznetsov, Gennady Leonov

chapter 10|5 pages

Capture of a Particle into Resonance

ByOleg Mikhailovich Kiselev

section 3|1 pages

Chaotic Data Analysis, Equations, and Applications

chapter 11|19 pages

Integral Equaions and Applications

ByAlexander G. Ramm

chapter 12|18 pages

Large-Time Behavior of Solutions to Evolution Equations

ByRamm Alexander G

chapter 14|20 pages

Characterization of Time Series Data

ByW. Kulp Christopher, J. Niskala Brandon

chapter 15|22 pages

Geometry of Local Instability in Hamiltonian Dynamics

ByM. Lewkowicz, J. Levitan, Y. Ben Zion, L. Horwitz

chapter 16|18 pages

Chaos Analysis of ER-Network Dynamics in Microscopy Imaging

ByTuan D. Pham, Wada Ikuo

chapter 18|11 pages

New Robust Stability of Discrete-Time Hybrid Systems

ByGrienggrai Rajchakit

section 4|1 pages

Chaos in Plasma

chapter 19|83 pages

Chaos in Plasma Physics

ByDan-Gheorghe Dimitriu, Maricel Agop

chapter 20|17 pages

Plasma Harmonic and Overtone Coupling

ByVictor J. Law

section 5|1 pages

Chaos in flows and Turbulence

chapter 21|24 pages

Wave Turbulence in Vibrating Plates

ByCadot Olivier, Ducceschi Michele, Humbert Thomas, Miquel Benjamin, Mordant Nicolas, Josserand Christophe, Touzé Cyril

chapter 22|44 pages

Nonlinear Dynamics of the Oceanic Flow

ByS.V. Prants, M.V. Budyansky, M.Yu. Uleysky

chapter 23|17 pages

The Suspensions of Maps to Flows

ByStarrett John

chapter 24|19 pages

Lagrangian Coherent Structures at the Onset of Hyperchaos in Two-Dimensional Flows

ByA. Miranda Rodrigo, L. Rempel Erico, C.-L. Chian Abraham, B. Schelin Adriane

section 6|1 pages

Chaos and Quantum Theory

chapter 26|26 pages

Application of Microwave Networks to Simulation of Quantum Graphs

ByŁawniczak Michał, Bauch Szymon, Sirko Leszek

section 7|1 pages

Optics and Chaos

chapter 27|40 pages

Optics and Chaos: Chaotic, Rogue, and Noisy Optical Dissipative Solitons

ByL. Vladimir, K. Kalashnikov

chapter 28|9 pages

Hyperbolic Prism, Poincaré Disk, and Foams

ByAlberto Tufaile, Adriana Pedrosa, Biscaia Tufaile

chapter 29|8 pages

Parhelic-Like Circle and Chaotic Light Scattering

ByAdriana Pedrosa

section 8|1 pages

Chaos Theory in Biology and Medicine

chapter 31|24 pages

Comb Models for Transport along Spiny Dendrites

ByMéndez Vicenç, Iomin Alexander

chapter 32|10 pages

Applications of Chaos Theory Methods in Clinical Digital Pathology

ByWlodzmierz Klonowski

section 9|1 pages

Chaos in Mechanical Sciences

chapter 33|16 pages

System Augmentation for Detection and Sensing: Theory and Applications

ByKiran D’Souza, Bogdan I. Epureanu

chapter 34|9 pages

Unveiling Complexity of Church Bells Dynamics Using Experimentally Validated Hybrid Dynamical Model

ByBrzeski Piotr, Kapitaniak Tomasz, Perlikowski Przemyslaw

section 10|1 pages

Chaotic Pattern Recognition

chapter 36|58 pages

The Science and Art of Chaotic Pattern Recognition

ByB. John Oommen, Qin Ke, Calitoiu Dragos

section 11|1 pages

Chaos in Socioeconomic and Human Sciences

chapter 37|22 pages

Why Economics Has Not Accomplished What Physics Has?

ByFaggini Marisa, Anna Parziale

chapter 38|51 pages

Human Fuzzy Rationality as a Novel Mechanism of Emergent Phenomena

ByIhor Lubashevsky

chapter 39|12 pages

Chaos in Monolingual and Bilingual Speech

ByElena Babatsouli

section 12|1 pages

Chaos In Music