For students who wish to study networked dynamical systems.
The course covers both classical results and very recent research.
You can find the course description at http://vlvz1.physik.hu-berlin.de/ws2018/physik/kvlinfo/de/?lvnummer=40497
and the location on the map.
Participation in the course requires that a student project is delivered.
Further details are going to appear soon at this place.
Requirements
The course is aimed at students that hold a bachelor degree in physics or mathematics.
Prior knowledge of the course Nonlinear Dynamics [P25.3.b] is helpful
but not necessary.
Semester Projects
The list of projects can be found here.
Syllabus
- Network basics
- A recap on dynamical systems
- Linear dynamics on networks: Diffusion
- Linear dynamics on networks: Master stability function
- Non-Linear dynamics on networks: Synchronisation
- ...
Script (in progress)
Find it here.
Suggested Reading
Complex Networks:
- Newman, M. E. J.Networks: An Introduction. (Oxford University Press, 2010).
- Jungnickel, D. Graphs, networks and algorithms. (Springer, 2005).
Dynamical Systems:
- Guckenheimer, J. \& Holmes, P. J. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences, Volume 42 (Springer-Verlag, 2002).
Dynamics on Networks
- Lovász, L. Random walks on graphs: A survey. Comb. Paul Erdos is Eighty 2, 1–46 (1993).
- Pikovsky, A., Rosenblum, M., Kurths, J. Synchronization: a universal concept in nonlinear sciences. Vol. 12. Cambridge university press, 2003.
Dynamics of Networks
- tba
Adaptive Networks
- tba