## Differential Equations, Dynamical Systems, and an Introduction to Chaos, Volume 60Thirty 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. * 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 |

### What people are saying - Write a review

#### Review: Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics)

User Review - Joecolelife - Goodreadsthis is an excellent introduction for beginners. in fact, this reference has explained the differential equations, the dynamical system and the chaos as clear as possible. the elementary mathematical ... Read full review

#### Review: Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics)

User Review - DJ - GoodreadsBig boy dynamical systems theory for once I've graduated from Strogatz's preschool. Read full review

### 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 |

407 | |

### Common terms and phrases

assume asymptotically stable attractor basic regions behavior of solutions bifurcations that occur canonical form Chapter circle closed orbit compute conjugacy Consider the system constant continuous coordinates defined denote dense Describe differential equations distinct eigenvalues dynamical systems eigenvalues eigenvector equilibrium point example exp(tA Figure ﬁnd first-order fixed point flow follows given graph harmonic oscillator Hence horseshoe map initial condition initial value problem iteration Liapunov function limit cycle linear map linearized system linearly independent logistic Lorenz system matrix nonautonomous nonlinear system Note nullclines open set origin parameter periodic points periodic solution phase portrait planar system plane Poincaré map population Proof Proposition Prove saddle sequence sink slope solution curve solution X(t solutions tend solve spiral subset subspace Suppose system of differential system X tangent theorem unstable curve vector field vector field points