Nonlinear Dynamics and Chaos

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind .

“"The new edition has a friendly yet clear technical style . . . 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 author's excellent use of geometric and graphical techniques greatly clarifies what can be amazingly complex behavior." -- Physics Today " Nonlinear Dynamics and Chaos is an excellent book that effectively demonstrates the power and beauty of the theory of dynamical systems. Its readers will want to learn more." -- Mathematical Association of America Praise for the prior edition: "Exceptionally well-written. Time after time, Strogatz gives explanations of concepts that are among the most lucid I have ever read...One of the best introductions to nonlinear dynamics currently available." -- SIAM Review "The examples impressed me with their subtlety and incisiveness. Important, delicate distinctions and exceptions are highlighted and accessible." -- Physics Today "More than any undergraduate book that I have seen in recent years, this book can lure students into the mathematical sciences, make them want to change their major, and spark in them some real intellectual curiosity." -- UMAP Journal”

"The new edition has a friendly yet clear technical style . . . 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 author's excellent use of geometric and graphical techniques greatly clarifies what can be amazingly complex behavior." Physics Today

"Nonlinear Dynamics and Chaos is an excellent book that effectively demonstrates the power and beauty of the theory of dynamical systems. Its readers will want to learn more." Mathematical Association of America

Steven Strogatz is the Schurman Professor of Applied Mathematics at Cornell University. His honours include MIT's highest teaching prize, a lifetime achievement award for the communication of mathematics to the general public, and membership in the American Academy of Arts and Sciences. His research on a wide variety of nonlinear systems,from synchronized fireflies to small-world networks,has been featured in the pages of Scientific American, Nature, Discover, Business Week, and The New York Times.

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind .

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