Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and EngineeringPaperback Studies in Nonlinearity
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- Publisher: PERSEUS BOOKS
- Format: Paperback | 512 pages
- Dimensions: 152mm x 234mm x 28mm | 726g
- Publication date: 19 January 2001
- Publication City/Country: Reading, MA
- ISBN 10: 0738204536
- ISBN 13: 9780738204536
- Sales rank: 40,490
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 the mathematical theory.Richly illustrated, and with many exercises and worked examples, this book is ideal for an introductory course at the junior/senior or first-year graduate level. It is also ideal for the scientist who has not had formal instruction in nonlinear dynamics, but who now desires to begin informal study. The prerequisites are multivariable calculus and introductory physics.
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Steven H. Strogatz is professor of applied mathematics at Cornell University. He received his Ph.D. from Harvard University in 1986. Professor Strogatz has been honored with several awards including MIT's highest teaching prize, the E.M. Baker Award for Excellence in Undergraduate Teaching, as well as a Presidential Young Investigator Award from the National Science Foundation. 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 .
The theory presented in this book is developed systematically, starting with first-order differential equations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, fractals and strange attractors.
Table of contents
* Overview One-Dimensional Flows * Flows on the Line * Bifurcations * Flows on the Circle * Flows on the Circle Two-Dimensional Flows * Linear Systems * Phase Plane * Limit Cycles * Bifurcations Revisited CHAOS * Lorenz Equations * One-Dimensional Maps * Fractals * Strange Attractors