Authors : Jean-René & Marc Monticelli
Overview
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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
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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
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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
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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?
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Bibliography
- Theorems & examples