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Nonlinear Dynamics and Chaos : With Applications to Physics, Biology, Chemistry, and Engineering
ISBN13:
by Strogatz, Steven H.
9780738204536
0738204536
Paperback
1/18/2001
PERSEUS BOOKS
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Summary
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 firstorder 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 firstyear 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.
Author Biography
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 systemsfrom synchronized fireflies to smallworld networkshas been featured in the pages of Scientific American, Nature, Discover, Business Week, and The New York Times .
Table of Contents
Preface  ix  

1  (14)  

1  (1)  

2  (2)  

4  (5)  

9  (6)  
Part I. OneDimensional Flows  

15  (29)  

15  (1)  

16  (2)  

18  (3)  

21  (3)  

24  (2)  

26  (2)  

28  (2)  

30  (2)  

32  (12)  

36  (8)  

44  (49)  

44  (1)  

45  (5)  

50  (3)  

53  (2)  

55  (6)  

61  (8)  

69  (4)  

73  (20)  

79  (14)  

93  (30)  

93  (1)  

93  (2)  

95  (1)  

96  (5)  

101  (2)  

103  (3)  

106  (17)  

113  (10)  
Part II. TwoDimensional Flows  

123  (22)  

123  (1)  

123  (6)  

129  (9)  

138  (7)  

140  (5)  

145  (51)  

145  (1)  

145  (3)  

148  (2)  

150  (5)  

155  (4)  

159  (4)  

163  (5)  

168  (6)  

174  (22)  

181  (15)  

196  (45)  

196  (1)  

197  (2)  

199  (4)  

203  (7)  

210  (1)  

211  (4)  

215  (26)  

227  (14)  

241  (60)  

241  (1)  

241  (7)  

248  (6)  

254  (6)  

260  (5)  

265  (8)  

273  (5)  

278  (23)  

284  (17)  
Part III. Chaos  

301  (47)  

301  (1)  

302  (9)  

311  (6)  

317  (9)  

326  (4)  

330  (5)  

335  (13)  

341  (7)  

348  (50)  

348  (1)  

349  (4)  

353  (4)  

357  (4)  

361  (5)  

366  (3)  

369  (10)  

379  (19)  

388  (10)  

398  (25)  

398  (1)  

399  (2)  

401  (3)  

404  (5)  

409  (2)  

411  (12)  

416  (7)  

423  (32)  

423  (1)  

423  (6)  

429  (5)  

434  (3)  

437  (4)  

441  (14)  

448  (7)  
Answers to Selected Exercises  455  (10)  
References  465  (10)  
Author Index  475  (3)  
Subject Index  478 