Steven H. Strogatz

Nonlinear Dynamics and Chaos

With Applications to Physics, Biology, Chemistry, and Engineering

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: CRC Press / Perseus Books
• Artikelnr. des Verlages: K376761
• 2. Aufl.
• Seitenzahl: 532
• Erscheinungstermin: 1. März 2015
• Englisch
• Abmessung: 228mm x 151mm x 30mm
• Gewicht: 1161g
• ISBN-13: 9780813349107
• ISBN-10: 0813349109
• Artikelnr.: 38077857

Autorenporträt

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.

Inhaltsangabe

1. Overview
PART I. ONE-DIMENSIONAL FLOWS
2. Flows on the Line
3. Bifurcations
4. Flows on the Circle
PART II. TWO-DIMENSIONAL FLOWS
5. Linear Systems
6. Phase Plane
7. Limit Cycles
8. Bifurcations Revisited
PART III. CHAOS
9. Lorenz Equations
10. One-Dimensional Maps
11. Fractals
12. Strange Attractors

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Preface 1. Overview 1.0 Chaos, Fractals, and Dynamics 1.1 Capsule History
of Dynamics 1.2 The Importance of Being Nonlinear 1.3 A Dynamical View of
the World PART I. ONE-DIMENSIONAL FLOWS 2. Flows on the Line 2.0
Introduction 2.1 A Geometric Way of Thinking 2.2 Fixed Points and Stability
2.3 Population Growth 2.4 Linear Stability Analysis 2.5 Existence and
Uniqueness 2.6 Impossibility of Oscillations 2.7 Potentials 2.8 Solving
Equations on the Computer Exercises 3. Bifurcations 3.0 Introduction 3.1
Saddle-Node Bifurcation 3.2 Transcritical Bifurcation 3.3 Laser Threshold
3.4 Pitchfork Bifurcation 3.5 Overdamped Bead on a Rotating Hoop 3.6
Imperfect Bifurcations and Catastrophes 3.7 Insect Outbreak Exercises 4.
Flows on the Circle 4.0 Introduction 4.1 Examples and Definitions 4.2
Uniform Oscillator 4.3 Nonuniform Oscillator 4.4 Overdamped Pendulum 4.5
Fireflies 4.6 Superconducting Josephson Junctions Exercises PART II.
TWO-DIMENSIONAL FLOWS 5. Linear Systems 5.0 Introduction 5.1 Definitions
and Examples 5.2 Classification of Linear Systems 5.3 Love Affairs
Exercises 6. Phase Plane 6.0 Introduction 6.1 Phase Portraits 6.2
Existence, Uniqueness, and Topological Consequences 6.3 Fixed Points and
Linearization 6.4 Rabbits versus Sheep 6.5 Conservative Systems 6.6
Reversible Systems 6.7 Pendulum 6.8 Index Theory Exercises 7. Limit Cycles
7.0 Introduction 7.1 Examples 7.2 Ruling Out Closed Orbits 7.3
Poincare-Bendixson Theorem 7.4 Lienard Systems 7.5 Relaxation Oscillators
7.6 Weakly Nonlinear Oscillators Exercises 8. Bifurcations Revisited 8.0
Introduction 8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations 8.2
Hopf Bifurcations 8.3 Oscillating Chemical Reactions 8.4 Global
Bifurcations of Cycles 8.5 Hysteresis in the Driven Pendulum and Josephson
Junction 8.6 Coupled Oscillators and Quasiperiodicity 8.7 Poincare Maps
Exercises PART III. CHAOS 9. Lorenz Equations 9.0 Introduction 9.1 A
Chaotic Waterwheel 9.2 Simple Properties of the Lorenz Equations 9.3 Chaos
on a

Rezensionen

"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