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. Strange Attractors, Bifurcation, and Related Theory. Chaotic Data Analysis, Equations, and Applications. Chaos in Plasma. Chaos in Flows and Turbulence. Chaos and Quantum Theory. Optics and Chaos. Chaos Theory in Biology and Medicine. Chaos in Mechanical Sciences. Chaotic Pattern Recognition. Chaos in Socioeconomic and Human Sciences. Chaos in Music. Index.
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.