Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, an important and exciting area that has shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview.
In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder.
Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
"This book is a readable tour and deep dive into chaotic dynamics and related concepts from the field of dynamical systems theory. Appropriate for use in a sequence at the undergraduate level, this book will also appeal to graduate students, postdocs, and faculty in the biological and social sciences and engineering."-James P. Crutchfield, University of California, Davis
"With clear and explanatory prose and simple yet precisely constructed examples, this book conveys a deep understanding of chaos, bifurcations, and other core concepts of dynamical systems to a much larger audience than was previously possible. Feldman achieves this all without relying on a deep knowledge of math. An impressive balancing act, this is certainly a significant contribution to the field."-Van Savage, University of California, Los Angeles
"Chaos and Dynamical Systems is a great introduction to nonlinear dynamics, bifurcations, and chaos. It is easy to follow and understand, yet also provides a generous amount of mathematical detail, which will satisfy technically oriented minds too. This book's core take-home message, that simple mathematical systems can produce complex dynamics, has implications for many real-world complex systems."-Hiroki Sayama, Binghamton University, State University of New York