Overview

• Foreword by Cédric Villani
• Preface

• A first tour through examples
  • Chapter 1 - The simplest example
  • Chapter 2 - The logistic equation
  • Chapter 3 - Sharks and sardines
  • Chapter 4 - The harmonic oscillator
  • Chapter 5 - A new look at the pendulum
  • Chapter 6 - Van der Pol’s periodic attractor
  • Chapter 7 - Chaotic attractor in an ‘ecosystem’ with two competing species eaten by a third one
  • Chapter 8 - What we have learnt so far
• Part I: One-dimensional systems: flows on the line
  • Chapter 1 - Prelude: graphical study of one-dimensional differential equations
  • Chapter 2 - Existence, uniqueness and lifetime of solutions
  • Chapter 3 - Fixed points & their stability
  • Chapter 4 - Interlude: Impossibility of periodic oscillations
  • Chapter 5 - Bifurcations: a first glance
• Part II: Two-dimensional systems: flows in the plane
  • Chapter 1 - Existence, uniqueness and lifetime of solutions
  • Chapter 2 - Phase portraits
  • Chapter 3 - Linear systems
  • Chapter 4 - Linearization: what happens near fixed points
  • Chapter 5 - Three examples from Biology
  • Chapter 6 - Interlude: for the pleasure of the eyes
  • Chapter 7 - Periodic oscillations & limit cycles
  • Chapter 8 - Bifurcations
  • Chapter 9 - A bunch of examples with limit cycles
  • Chapter 10 - Stability of Fixed Points & the Lyapunov method
  • Chapter 11 - Interlude: no chaos for two-dimensional systems
• Part III: Beyond flows in the plane: quasi-periodicity & chaos
  • Chapter 1 - The Lorenz attractor
  • Chapter 2 - The Rössler attractor
  • Chapter 3 - Four more strange attractors
  • Chapter 4 - From quasiperiodicity to chaos
• What next?
  • A discrete-time prey-predator model
  • Turing’s patterns
  • Julia Sets
• Bibliography
• Theorems & examples
  • The Rosenzweig-McArthur model
  • The idealized pendulum
  • Building a limit cycle from scratch
  • Lyapunov’s theorem
  • Hartman-Grobman Theorem
  • Poincaré-Bendixson theorem
  • Andronov-Hopf bifurcation theorem