Nonlinear dynamics and chaos : with applications to physics, biology, chemistry, and engineering
著者
書誌事項
Nonlinear dynamics and chaos : with applications to physics, biology, chemistry, and engineering
（Studies in nonlinearity）
Perseus Books, 2000, c1994
- : pbk
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注記
Publisher varies: [Boulder, Colo.] : Westview press , 2000
"First paperback printing, December 2000"--T.p. verso
"Westview Press, A Member of Perseus Books"
Includes bibliographical references (p. 465-474) and indexes
内容説明・目次
内容説明
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.
目次
* 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
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