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

Advanced students and practitioners in higher mathematics.

Preface First Order Equations Planar Linear Systems Phase Portraits for Planar Systems Classification of Planar Systems Higher Dimensional Linear Algebra Higher Dimensional Linear Systems Nonlinear Systems Equilibria in Nonlinear Systems Global Nonlinear Techniques Closed Orbits and Limit Sets Applications in Biology Applications in Circuit Theory Applications in Mechanics The Lorenz System Discrete Dynamical Systems Homoclinic Phenomena Existence and Uniqueness Revisited