Mathematics for Complex Systems 2014

The course covers some basic topics required to gain an analytical understanding of some aspects of complex systems. Most emphasis is put on an introduction to nonlinear dynamics (and its relationship to various models of complex systems). In the second part of the course some topics around models of complex networks and their relationship to complexity science will be discussed.

Links to lecture slides (some slides cover more than one lecture):

Lecture 1. Problem sheet for Lecture 1

• some python scripts used in lecture 1
  • a script to numerically integrate a 1d ODE in python
  • a script to numerically integrate 2d zombie dynamics in python
  • example script to draw vector fields in python

Lecture 2. Problem sheet for Lecture 2

Lecture 3.

Lecture 4.

Lecture 5. Problem sheet for Lectures 4-5

Lecture 6.

Lecture 7. in-class test

Lecture 8.

Some recommended reading for the course:

• Dynamical Systems
  • The lecture mainly follows the book by Steven Strogatz and won't offer a precise treatment of many mathematical aspects. The emphasis is on an intutive understanding of the problems and methods.
    • Strogatz, “Nonlinear Dynamics and Chaos” , Westview Press
  • A much more precise and comprehensive treatment can, e.g., be found in:
    • Arrowsmith and Place, "An introduction to Dynamical Systems", Cambridge University Press
    • Guckenheimer and Holmes, "Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields", Springer
• Networks
  • Newman, “Networks: An Introduction”, Oxford University Press