Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Steven H. Strogatz, Westview Press, 2015. 2nd ed. $60.00 paper (528 pp.). ISBN 978-0-813-34910-7 Buy at Amazon
It’s clear from the books he has written that Steven Strogatz—a prolific and able writer and a professor of applied mathematics at Cornell University—has broad interests and knowledge in many scientific fields, including physics: In 2014 he was elected an American Physical Society Fellow. For popular audiences, he has penned such engaging works as Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life (Hachette Books, 2003) and The Joy of “x”: A Guided Tour of Math, from One to Infinity (Houghton Mifflin, 2012).
Strogatz’s latest book, Nonlinear Dynamics and Chaos (2nd edition), is aimed broadly at scientists and engineers and is suitable as an undergraduate or graduate course textbook. That’s no accident since much of the content of this book, and the first edition (Westview Press, 1994), originated from a course Strogatz taught at MIT and Cornell. The new edition has a friendly yet clear technical style; it feels like concepts are not just printed on the page but are being spoken to the reader. Strogatz enhances his already engaging tone with historical notes and nods to things not yet understood, in the same way a good lecturer enlivens a class discussion. A course based on this book could be an excellent elective in a physics department; it might even draw students from other STEM fields due to the intrinsic interest of the material or the usefulness of its techniques.
In presenting the subject, the author draws from the past 30 years of developments that have advanced our understanding of dynamics beyond the linear examples—for instance, harmonic oscillators—that permeate current physics curricula. The advances came from theoretical and computational scholars, and the book does a great job of acknowledging them. The methods and techniques that form the bulk of the book’s content apply useful concepts—bifurcations, phase-space analysis, and fractals, to name a few—that have been widely adopted in physics, biology, chemistry, and engineering. One of the book’s biggest strengths is that it explains core concepts through practical examples drawn from various fields and from real-world systems; the examples include pendula, Josephson junctions, chemical oscillators, and convecting atmospheres. The illustrations, in particular, have been enhanced in the new edition.
The techniques needed to understand the behavior of nonlinear systems are inherently mathematical. Fortunately, the author’s excellent use of geometric and graphical techniques greatly clarifies what can be amazingly complex behavior. For example, in carefully working through the development and behavior of the Lorenz equations, Strogatz introduces a simple waterwheel machine as a model to help define terms and tie together such key concepts as fixed points, bifurcations, chaos, and fractals. The reader gets a feel for the science behind the differential equations. Moreover, for each concept, the mathematics is accompanied by clear figures and nicely posed student exercises.
This is fast becoming a staple book among practitioners of nonlinear dynamics. Both my theory and experimental colleagues often recommend it to their students. Other books in the same genre are worth mentioning: Edward Ott’s Chaos in Dynamical Systems (2nd edition, Cambridge University Press, 2002) is an excellent introduction at a graduate level, and Robert Hilborn’s Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers (2nd edition, Oxford University Press, 2001) is quite reader friendly. This second edition of Nonlinear Dynamics and Chaos is a great addition to our communal bookshelf. It serves for a wide range of uses and will be of interest to audiences with diverse backgrounds and levels of expertise.
Daniel Lathrop is a physics professor at the University of Maryland in College Park. He and his research group conduct nonlinear-dynamics and geophysics experiments.