Exploring Chaos

This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. It describes the theory of fractals, focusing on the importance of scaling and ordinary differential equations.

Chaos theory is giving scientists fresh insights into all sorts of unruly phenomena-from dripping faucets to swinging pendulums, from the vagaries of the weather to the movements of the planets, from heart rhythms to gold futures. In this collection of front-line reports, edited for the general reader, internationally recognized experts such as Ian Stewart, Robert M. May, and Benoit Mandelbrot draw on the latest research to trace the roots of chaos in modern science and mathematics.

This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. It describes the theory of fractals, focusing on the importance of scaling and ordinary differential equations.

This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures. "This book will be of valuable help for my lectures" Hermann Haken, Stuttgart "This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg “This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, Germany

DIVApplications of chaos theory in political science, economics, and sociology /div

It's no secret that we are addicted to control. We work to control our time, our TVs, our weight, and even our faith lives. We strive for efficiency and quantifiable results. But all that control, we soon find out, is exhausting. And it is contrary to God's plan for us. In Chaos and Grace, Mark Galli offers readers freedom from the need for control and order by reintroducing them to the mysterious work of the Holy Spirit. In this insightful book, Galli exposes our individual mistakes and the church's foibles and points the way to grace--which, as it happens, usually lies through chaos and crisis. Through Scripture he shows us that this problem is not unique to modern believers and helps us learn from the stories of God's people through the ages as they gave up and gave in to the transforming work of the Holy Spirit.

Psychology and the social sciences are in need of a new foundation, one that provides a better model for understanding complex behavior. Chaos theory and its newest permutation, complexity theory, offers an innovative, exciting and potentially revolutionary leap forward in the evolution of scientific thought. In Clinical Chaos, therapists and theoreticians from various areas in the social sciences will explore the relevance and implications for non-linear dynamics in observing, explaining, and understanding human behavior. At last, the scientific search can again encompass surprise, transformation, unpredictability, and pattern. This book is intended to introduce social scientists to chaos through paths that are already familiar. By linking chaos theory with existing psychological theories and established areas of clinical pursuit, Clinical Chaos emphasizes the relevance of this new science in providing a more flexible useful model for complexities of life.

The science of chaos attracts the attention of researchers in many disciplines. The idea: by following simple principles of randomness and disorder, patterns emerge. Here, users on their own PC's can construct mathematical models duplicating processes found in nature.