An Introduction to Chaotic Dynamics

Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. While the rules describing chaotic dynamical systems are well-specified and simple, the behaviour of many such systems is remarkably complex and produces output that appears random and for which long-term prediction is limited. As well as a branch of mathematics, it is critical in the understanding of many actual-world systems and in applications in fields such as computer science, geology, engineering, meteorology, physics, population dynamics, robotics, biology, politics, philosophy and economics.

The book begins by laying out preliminary material needed to understand the literature on chaos (e.g., randomness, uncertainty, determinism, dynamical systems, state spaces, attractors, nonlinear dynamics, sensitive dependence, modelling). This provides the background that any reader would need to be able to navigate the literature. It goes on to discuss the history of the field, the different definitions of chaos, and the implications of chaos for modelling phenomena and forecasting system behaviour along with the differences between classical and quantum chaos. The book then rounds out with broader implications. Does chaos forces scientists into new forms of explanation or simply variations on explanatory patterns we've already been using?

The book helps fill the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians. This book will be useful to students at the undergraduate and advanced levels, but also to researchers in the physical, social, and biological sciences needing more conceptual introduction to chaos and chaotic systems.