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Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering 2nd edition [Minkštas viršelis]

4.38/5 (1579 ratings by Goodreads)
(Mathematics Department, Cornell University)
  • Formatas: Paperback / softback, 532 pages, aukštis x plotis: 229x152 mm, weight: 840 g
  • Išleidimo metai: 01-Mar-2015
  • Leidėjas: Westview Press Inc
  • ISBN-10: 0813349109
  • ISBN-13: 9780813349107
Kitos knygos pagal šią temą:
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering 2nd editionDidesnis paveikslėlis
  • Formatas: Paperback / softback, 532 pages, aukštis x plotis: 229x152 mm, weight: 840 g
  • Išleidimo metai: 01-Mar-2015
  • Leidėjas: Westview Press Inc
  • ISBN-10: 0813349109
  • ISBN-13: 9780813349107
Kitos knygos pagal šią temą:
Kitos knygos iš šio išskirtinio pasiūlymo: Taylor & Francis siūlo daug technologijos knygų ISE (International Student Edition) kainomis
Pastovi nuoroda: https://www.kriso.lt/db/9780813349107.html
Raktažodžiai:
An accessible introduction to chaos and nonlinear systems, with numerous examples, illustrations, and applications to science and engineering.


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.

Recenzijos

"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

Preface to the Second Edition   ix  
Preface to the First Edition   xi  
  1 Overview
  1 (14)
  1.0 Chaos, Fractals, and Dynamics
  1 (1)
  1.1 Capsule History of Dynamics
  2 (2)
  1.2 The Importance of Being Nonlinear
  4 (5)
  1.3 A Dynamical View of the World
  9 (6)
Part I One-Dimensional Flows  
  2 Flows on the Line
  15 (30)
  2.0 Introduction
  15 (1)
  2.1 A Geometric Way of Thinking
  16 (2)
  2.2 Fixed Points and Stability
  18 (3)
  2.3 Population Growth
  21 (3)
  2.4 Linear Stability Analysis
  24 (2)
  2.5 Existence and Uniqueness
  26 (2)
  2.6 Impossibility of Oscillations
  28 (2)
  2.7 Potentials
  30 (2)
  2.8 Solving Equations on the Computer
  32 (4)
  Exercises for
Chapter 2
  36 (9)
  3 Bifurcations
  45 (50)
  3.0 Introduction
  45 (1)
  3.1 Saddle-Node Bifurcation
  46 (5)
  3.2 Transcritical Bifurcation
  51 (3)
  3.3 Laser Threshold
  54 (2)
  3.4 Pitchfork Bifurcation
  56 (6)
  3.5 Overdamped Bead on a Rotating Hoop
  62 (8)
  3.6 Imperfect Bifurcations and Catastrophes
  70 (4)
  3.7 Insect Outbreak
  74 (6)
  Exercises for
Chapter 3
  80 (15)
  4 Flows on the Circle
  95 (30)
  4.0 Introduction
  95 (1)
  4.1 Examples and Definitions
  95 (2)
  4.2 Uniform Oscillator
  97 (1)
  4.3 Nonuniform Oscillator
  98 (5)
  4.4 Overdamped Pendulum
  103 (2)
  4.5 Fireflies
  105 (4)
  4.6 Superconducting Josephson Junctions
  109 (6)
  Exercises for
Chapter 4
  115 (10)
Part II Two-Dimensional Flows  
  5 Linear Systems
  125 (21)
  5.0 Introduction
  125 (1)
  5.1 Definitions and Examples
  125 (6)
  5.2 Classification of Linear Systems
  131 (8)
  5.3 Love Affairs
  139 (3)
  Exercises for
Chapter 5
  142 (4)
  6 Phase Plane
  146 (52)
  6.0 Introduction
  146 (1)
  6.1 Phase Portraits
  146 (3)
  6.2 Existence, Uniqueness, and Topological Consequences
  149 (2)
  6.3 Fixed Points and Linearization
  151 (5)
  6.4 Rabbits versus Sheep
  156 (4)
  6.5 Conservative Systems
  160 (4)
  6.6 Reversible Systems
  164 (4)
  6.7 Pendulum
  168 (6)
  6.8 Index Theory
  174 (7)
  Exercises for
Chapter 6
  181 (17)
  7 Limit Cycles
  198 (46)
  7.0 Introduction
  198 (1)
  7.1 Examples
  199 (2)
  7.2 Ruling Out Closed Orbits
  201 (4)
  7.3 Poincare-Bendixson Theorem
  205 (7)
  7.4 Lienard Systems
  212 (1)
  7.5 Relaxation Oscillations
  213 (4)
  7.6 Weakly Nonlinear Oscillators
  217 (13)
  Exercises for
Chapter 7
  230 (14)
  8 Bifurcations Revisited
  244 (65)
  8.0 Introduction
  244 (1)
  8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations
  244 (7)
  8.2 Hopf Bifurcations
  251 (6)
  8.3 Oscillating Chemical Reactions
  257 (7)
  8.4 Global Bifurcations of Cycles
  264 (4)
  8.5 Hysteresis in the Driven Pendulum and Josephson Junction
  268 (8)
  8.6 Coupled Oscillators and Quasiperiodicity
  276 (5)
  8.7 Poincare Maps
  281 (6)
  Exercises for
Chapter 8
  287 (22)
Part III Chaos  
  9 Lorenz Equations
  309 (46)
  9.0 Introduction
  309 (1)
  9.1 A Chaotic Waterwheel
  310 (9)
  9.2 Simple Properties of the Lorenz Equations
  319 (6)
  9.3 Chaos on a Strange Attractor
  325 (8)
  9.4 Lorenz Map
  333 (4)
  9.5 Exploring Parameter Space
  337 (5)
  9.6 Using Chaos to Send Secret Messages
  342 (6)
  Exercises for
Chapter 9
  348 (7)
  10 One-Dimensional Maps
  355 (50)
  10.0 Introduction
  355 (1)
  10.1 Fixed Points and Cobwebs
  356 (4)
  10.2 Logistic Map: Numerics
  360 (4)
  10.3 Logistic Map: Analysis
  364 (4)
  10.4 Periodic Windows
  368 (5)
  10.5 Liapunov Exponent
  373 (3)
  10.6 Universality and Experiments
  376 (10)
  10.7 Renormalization
  386 (8)
  Exercises for
Chapter 10
  394 (11)
  11 Fractals
  405 (24)
  11.0 Introduction
  405 (1)
  11.1 Countable and Uncountable Sets
  406 (2)
  11.2 Cantor Set
  408 (3)
  11.3 Dimension of Self-Similar Fractals
  411 (5)
  11.4 Box Dimension
  416 (2)
  11.5 Pointwise and Correlation Dimensions
  418 (5)
  Exercises for
Chapter 11
  423 (6)
  12 Strange Attractors
  429 (31)
  12.0 Introduction
  429 (1)
  12.1 The Simplest Examples
  429 (6)
  12.2 Flenon Map
  435 (5)
  12.3 Rossler System
  440 (3)
  12.4 Chemical Chaos and Attractor Reconstruction
  443 (4)
  12.5 Forced Double-Well Oscillator
  447 (7)
  Exercises for
Chapter 12
  454 (6)
Answers to Selected Exercises   460 (10)
References   470 (13)
Author Index   483 (4)
Subject Index   487  
Steven Strogatz is the Schurman Professor of Applied Mathematics at Cornell University. His honors 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.