Chaos

Text by Will Bradley, Brian Sholis, Chris Jennings.

This book discusses dynamical systems that are typically driven by stochastic dynamic noise. It is written by two statisticians essentially for the statistically inclined readers. It covers many of the contributions made by the statisticians in the past twenty years or so towards our understanding of estimation, the Lyapunov-like index, the nonparametric regression, and many others, many of which are motivated by their dynamical system counterparts but have now acquired a distinct statistical flavor.

One of the bestselling books on Chaos/Fractals examines chaos theory in a much more practical way than other books. Chaos is not just a way of generating computer graphics, or a mathematical curiosity. It has relevance to the real world and the easiest way to explore and visualize chaos is on the computer screen.

Table of contents: 1. Introduction. 2. Mappings. 3. Flows. 1. Two-variable systems. 4. Flows II. Three-vairable systems. 5. Forced systems. 6. Coupled systems. 7.Experimental methods. 8. The Belousov-Zhabotinskii reaction and other solution-phase reactions. 9. Gas-phase reactions. 10. Heterogeneous catalysis. 11. Electrodissolution reactions. 12. Biochemical systems. Index.

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

Computerized combat models are known occasionally to exhibit non-monotonic behavior in the sense that adding capabilities to one of the combatants degrades rather than improves the battle outcome for that side. Using a simple combat model, this report shows that for an important class of (nonlinear) combat phenomena--reinforcement decisions based on the state of the battle--such non-monotonicities can be widespread and are related to mathematically chaotic behavior caused by the nonlinearities. Unlike other common sources of non-monotonicity, the latter makes ameliorating the non-monotonicities difficult. This report also demonstrates that larger, more complex models are not immune to these effects. The emerging understanding of these effects has serious implications for the verification of models that are to be used for comparative purposes.

Katya Walter, Ph.D. examines the new nonlinear science of Chaos theory and finds there a broad new highway to God. At the deepest level of mathematical structure, there is a union of new physics (Chaos theory), new biology (the genetic code map), and the ancient wisdom of I Ching.Like I Ching, Chaos and the genetic code are both yin and yang -- interplay of opposites.

The story of a self-sufficient community founded at the end of the 1960s by a bunch of university drop-outs, and of their first born - Chaos, a mixture of Swampy, John Lennon, Bob Geldof and Princess Diana.

The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.

This is the first book-length study of William James’ style, arguing that the manner in which James writes The Principles of Psychology and The Varieties of Religious Experience serves to construct a chaotic world for his readers. The book examines the uses of chaos in western literature and philosophy and reaches two conclusions: that chaos may be “utter confusion and disorder,” but, paradoxically, that disorder is communicated through some particular order — in Joyce’s term, all chaos is “chaosmos.” Secondly, what is essential about chaos is what it does: nothing is inherently chaotic, rather chaos is used to contrast with or challenge something that is more structured or formed. Finally, the author presents an examination of the religious function of James’ chaotic worldview as a disorientation which orients.

Most genetics textbooks deal adequately with plant and animal genetics, but tend to neglect fungi except for two areas. Firstly, the ascus segregations which, in the 1960s, contributed so much to developing an understanding of the mechanism of recombination and secondly, the contribution that work on yeast (as a model eukaryote) is currently making to understanding cell cycle control and its genetic regulation. Consequently, most introductory genetics texts will leave the reader/student with the impression that fungi are of use when peculiarities of their structure or life style suit them to particular experimental approaches, but are not worth mentioning otherwise. The authors have produced a book that will compensate for this imbalance. This book discusses the genetics of fungi, or mycology, in a way that is attractive and challenging, succinct yet comprehensive, sensitive to commercial and applied aspects, yet also theoretical, dealing with their genetics from molecules to individuals to population. This short text will be an ideal supplement to the established basic textbooks in genetics or can be used as the sole text for an advanced course devoted to fungal genetics.

Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular. Contents: Poincaré Map Technique, Smale Horseshoe, and Symbolic DynamicsRobustness of ChaosStatistical Properties of Chaotic AttractorsStructural StabilityTransversality, Invariant Foliation, and the Shadowing LemmaChaotic Attractors with Hyperbolic StructureRobust Chaos in Hyperbolic SystemsLorenz-Type SystemsRobust Chaos in the Lorenz-Type SystemsNo Robust Chaos in Quasi-AttractorsRobust Chaos in One-Dimensional MapsRobust Chaos in 2-D Piecewise Smooth Maps Readership: Advanced undergraduate and graduate students, researchers, engineers and instructors interested in chaos and dynamical systems. Keywords:Poincaré;Map Technique;Smale Horseshoe;Symbolic Dynamics;Robustness of Chaos;Statistical Properties of Chaotic Attractors;Structural Stability Transversality;Invariant Foliation;Shadowing Lemma;Hyperbolic Structure;Lorenz-Type Systems;Quasi-Attractors;Robust Chaos in One Dimensional Maps;Robust Chaos in 2-D Piecewise Smooth Maps

Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.

For centuries, humankind has believed that the world with all its form and structure was created by supernatural forces. In recent decades science has shaken these beliefs with the discovery of the exciting possibility of a self-created and self-creating world — of self-organization. Synergetics endeavours to reveal the intimate mechanisms of self-organization. The transitions from chaos to order, the nature of self-organization, the various approaches to it and certain philosophical inferences are outlined. Synergetics thus represents a remarkable confluence of many strands of thought, and has become a paradigm in modern culture. This book exposes the reader to striking new vistas in physics and mathematics, chemistry and biology, social sciences and philosophy — all interlocked around the concept of self-organization.

In this book, leading researchers present their current work in the challenging area of chaos control in nonlinear circuits and systems, with emphasis on practical methodologies, system design techniques and applications. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this area. The scope and aim of this book are to bridge the gap between chaos control methods and circuits and systems. It is an ideal starting point for anyone who needs a fundamental understanding of controlling chaos in nonlinear circuits and systems.

God's shadow, or the dark Self, is connected to death, destruction and madness. Paradoxically, it is also indispensable to life. At a time when our highest values are turning against us, the psychological message of this book is a beacon of hope.