Differential Equations, Dynamical Systems, and an Introduction to Chaos - 2nd Edition - ISBN: 9780080491141

Differential Equations, Dynamical Systems, and an Introduction to Chaos

2nd Edition

eBook ISBN: 9780080491141
Imprint: Academic Press
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Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.

The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems.

Key Features

  • 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 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.

Table of Contents

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


Academic Press
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"The exposition is excellent. I particularly liked how the proofs are fairly easy to follow... There are several instances where 'What if...?' questions come up naturally and the authors explore these as though they were reading your mind." - Gareth Roberts, Holy Cross "This text contains exactly what a student entering graduate school in Dynamical Systems needs to know; it is Dynamical Systems from three mathematicians who are not only among the world's most prominent experts in dynamical systems, but who are also among the world's best mathematical expositors. The book contains the benchmark models of chaos to which much of current research is compared" - Bruce Peckham, University of Minnesota "The presentation is very clear and often supported by carefully selected key-examples. The book meets very high pedagogical standards and certainly is a worthy successor of the original version." -R. Steinbauer, Wien, in MONATSHEFTE FUR MATHEMATIC, VOL 147