Authors : JeanRené Chazottes & Marc Monticelli
Overview

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: Onedimensional systems: flows on the line
 Chapter 1  Prelude: graphical study of onedimensional 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: Twodimensional 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 twodimensional systems

Part III: Beyond flows in the plane: quasiperiodicity & 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?

Bibliography
 Theorems & examples