Differential Equations, Dynamical Systems, and an Introduction to Chaos, Volume 60

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Academic Press, 2004 - Mathematics - 417 pages
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Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition, provides a rigorous yet accessible introduction to differential equations and dynamical systems.

The original text by three of the world's leading mathematicians has become the standard textbook for graduate courses in this area. Thirty years in the making, this Second Edition brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.

The book explores the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It presents the simplification of many theorem hypotheses and includes bifurcation theory throughout. It contains many new figures and illustrations; a simplified treatment of linear algebra; detailed discussions of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor; and increased coverage of discrete dynamical systems.

This book will be particularly useful to advanced students and practitioners in higher mathematics.



* Developed by award-winning researchers and authors
* Provides a rigorous yet accessible introduction to differential equations and dynamical systems
* Includes bifurcation theory throughout
* Contains numerous explorations for students to embark upon

NEW IN THIS EDITION
* New contemporary material and updated applications
* Revisions throughout the text, including simplification of many theorem hypotheses
* Many new figures and illustrations
* Simplified treatment of linear algebra
* Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor
* Increased coverage of discrete dynamical systems
 

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Contents

Chapter 1 FirstOrder Equations
1
Chapter 2 Planar Linear Systems
21
Chapter 3 Phase Portraits for Planar Systems
39
Chapter 4 Classification of Planar Systems
61
Chapter 5 Higher Dimensional Linear Algebra
75
Chapter 6 Higher Dimensional Linear Systems
107
Chapter 7 Nonlinear Systems
139
Chapter 8 Equilibria in Nonlinear Systems
159
Chapter 11 Applications in Biology
235
Chapter 12 Applications in Circuit Theory
257
Chapter 13 Applications in Mechanics
277
Chapter 14 The Lorenz System
303
Chapter 15 Discrete Dynamical Systems
327
Chapter 16 Homoclinic Phenomena
359
Chapter 17 Existence and Uniqueness Revisited
383
Bibliography
407

Chapter 9 Global Nonlinear Techniques
189
Chapter 10 Closed Orbits and Limit Sets
215

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