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Handbook of Applications of Chaos Theory

Edited by: Christos H. Skiadas , Charilaos Skiadas

Print publication date:  June  2016
Online publication date:  June  2016

Print ISBN: 9781466590434
eBook ISBN: 9781466590441
Adobe ISBN:

10.1201/b20232
 Cite  Marc Record

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

Chapter  1:  The Intermittency Route to Chaos Download PDF
Chapter  2:  Deterministic Chaos and Evolutionary Dynamics: Mutual Relations Download PDF
Chapter  3:  On the Transition to Phase Synchronized Chaos Download PDF
Chapter  4:  The Kolmogorov–Taylor Law of Turbulence: What Can Rigorously Be Proved? Download PDF
Chapter  5:  Nonlinear Dynamics of Two-Dimensional Chaotic Maps and Fractal Sets for Snow Crystals Download PDF
Chapter  6:  Fractional Chen Oscillators Download PDF
Chapter  7:  Strange Attractors and Classical Stability Theory: Stability, Instability, Lyapunov Exponents and Chaos Download PDF
Chapter  8:  Numerical Visualization of Attractors: Self-Exciting and Hidden Attractors Download PDF
Chapter  9:  Bifurcation Analysis of a Simple 3D BVP Oscillator and Chaos Synchronization of Its Coupled Systems Download PDF
Chapter  10:  Capture of a Particle into Resonance Download PDF
Chapter  11:  Integral Equations and Applications Download PDF
Chapter  12:  Large-Time Behavior of Solutions to Evolution Equations Download PDF
Chapter  13:  Empirical Wavelet Coefficients and Denoising of Chaotic Data in the Phase Space Download PDF
Chapter  14:  Characterization of Time Series Data Download PDF
Chapter  15:  Geometry of Local Instability in Hamiltonian Dynamics Download PDF
Chapter  16:  Chaos Analysis of ER-Network Dynamics in Microscopy Imaging Download PDF
Chapter  17:  Supersymmetric Theory of Stochastics: Demystification of Self-Organized Criticality Download PDF
Chapter  18:  New Robust Stability of Discrete-Time Hybrid Systems Download PDF
Chapter  19:  Chaos in Plasma Physics Download PDF
Chapter  20:  Plasma Harmonic and Overtone Coupling Download PDF
Chapter  21:  Wave Turbulence in Vibrating Plates Download PDF
Chapter  22:  Nonlinear Dynamics of the Oceanic Flow Download PDF
Chapter  23:  The Suspensions of Maps to Flows Download PDF
Chapter  24:  Lagrangian Coherent Structures at the Onset of Hyperchaos in Two-Dimensional Flows Download PDF
Chapter  25:  Chaotic Interference versus Decoherence: External Noise, State Mixing, and Quantum-Classical Correspondence Download PDF
Chapter  26:  Application of Microwave Networks to Simulation of Quantum Graphs Download PDF
Chapter  27:  Optics and Chaos: Chaotic, Rogue, and Noisy Optical Dissipative Solitons Download PDF
Chapter  28:  Hyperbolic Prism, Poincaré Disk, and Foams Download PDF
Chapter  29:  Parhelic-Like Circle and Chaotic Light Scattering Download PDF
Chapter  30:  Applications of Extreme Value Theory in Dynamical Systems for the Analysis of Blood Pressure Data Download PDF
Chapter  31:  Comb Models for Transport along Spiny Dendrites Download PDF
Chapter  32:  Applications of Chaos Theory Methods in Clinical Digital Pathology Download PDF
Chapter  33:  System Augmentation for Detection and Sensing: Theory and Applications Download PDF
Chapter  34:  Unveiling Complexity of Church Bells Dynamics Using Experimentally Validated Hybrid Dynamical Model Download PDF
Chapter  35:  Multiple Duffing Problems Based on Hilltop Bifurcation Theory on MFM Models Download PDF
Chapter  36:  The Science and Art of Chaotic Pattern Recognition Download PDF
Chapter  37:  Why Economics Has Not Accomplished What Physics Has? Download PDF
Chapter  38:  Human Fuzzy Rationality as a Novel Mechanism of Emergent Phenomena Download PDF
Chapter  39:  Chaos in Monolingual and Bilingual Speech Download PDF
Chapter  40:  Composers and Chaos: A Survey of Applications of Chaos Theory in Musical Arts and Research Download PDF
prelims Download PDF
Index Download PDF
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