Differential Equations, Dynamical Systems, and an Introduction to Chaos
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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Chapter 1 FirstOrder Equations
Chapter 2 Planar Linear Systems
Chapter 3 Phase Portraits for Planar Systems
Chapter 4 Classification of Planar Systems
Chapter 5 Higher Dimensional Linear Algebra
Chapter 6 Higher Dimensional Linear Systems
Chapter 7 Nonlinear Systems
Chapter 8 Equilibria in Nonlinear Systems
Chapter 11 Applications in Biology
Chapter 12 Applications in Circuit Theory
Chapter 13 Applications in Mechanics
Chapter 14 The Lorenz System
Chapter 15 Discrete Dynamical Systems
Chapter 16 Homoclinic Phenomena
Chapter 17 Existence and Uniqueness Revisited