direkt zum Inhalt springen

direkt zum Hauptnavigationsmenü

Sie sind hier

TU Berlin

Page Content

There is no English translation for this web page.

Networks (with applications to neuroscience)

Lecture in the summer term 2011

Staff: Dr. Philipp Hövel

Start: June 6, 2011

Tentative dates:

Mondays: (6.6, (13.6.), 20.6.): 9:00 - 13:00
Tuesdays: (7.6., 14.6., 21.6.): 9:00 - 13:00
Fridays: (10.6., 17.6., 24.6.): 14:00 - 15:30

Room: BCCN lecture hall (Haus 6), Philippstr. 13, 10115 Berlin (directions, campus map)

For students of the Physics Programme (Master and Diplom-Hauptstudium), the International Master Program Computational Neuroscience as well as interested members of Graduiertenkolleg 1558 (Nonequilibrium Collective Dynamics in Condensed Matter and Biological Systems) and the Sonderforschungsbereich 910 (Control of self-organizing nonlinear systems: Theoretical methods and concepts of application).

When attending this course 3 credit points within the ECTS system can be obtained.

For physics students (MSc): This course can be combined with a course on Theoretische Physik VI: Vertiefung, e.g., Nichtgleichgewichtsstatistik (WS 2010/11) to a physikalischen Wahlpflichtmodul (grundlagenorientierte Studienrichtung).

Another lecture with the related topic "Nichtlineare Dynamik in Physiologie und Medizin" is given by Dr. Markus Dahlem.


A tentative outline looks as follows:

  • Frist week:
    Monday (6.6.):
    Preliminaries, Introduction, Network characteristics
    Tuesday (7.6.): Network topologies (random, regular, lattice, small-world)
    Friday (10.6.): Graph theory
  • Second week:
    Monday (13.6.):
    No lecture due to holiday
    Tuesday (14.6.): Social networks (robustness, mobility)
    Friday (17.6.): Epidemics, disease prediction
  • Third week:
    Monday (20.6.):
    Neural models, network motifs, time delays
    Tuesday (21.6.): Synchronization in neural networks, reconstruction of networks (based on predefined spike patterns)
    Friday (24.6.): Master stability function, wrap up, NetEvo software
  • Fourth week:
    Monday (27.6.):
    Oral examinations


  • Active participation
  • Solving exercise sheets
  • Benotete Scheine can be obtained on the basis of an oral examination (during the week of Monday, June 27)


Visualizations for nonlinear dynamics (including the FitzHugh-Nagumo model) can be found here: OWL project.

Exercise Sheets

Due date
Network characteristics
Graph theory
SIS model
Reaction-diffusion, Master stability function formalism

Office hours

Office hours

TU Berlin: EW 633
Tue: 13:00 - 14:00
BCCN: 0.24 (Haus 2)
by appointment


Literature concerning the topic of this lecture:

Further references on nonlinear dynamics in general:

  • Vadim S. Anishchenko: Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments (Springer Series in Synergetics)
  • Luigi Fortuna: From Physics to Control Through an Emergent View (World Scientific Series on Nonlinear Science, Series B)
  • Heinz Georg Schuster: Reviews of Nonlinear Dynamics and Complexity: Volume 1 (Annual Reviews of Nonlinear Dynamics and Complexity)
  • Heinz Georg Schuster: Reviews of Nonlinear Dynamics and Complexity: Volume 2 (Annual Reviews of Nonlinear Dynamics and Complexity (Vch))
  • Heinz Georg Schuster: Reviews of Nonlinear Dynamics and Complexity: Volume 3 (Annual Reviews of Nonlinear Dynamics and Complexity (Vch))
  • Fatihcan M. Atay, Complex Time-Delay Systems, Springer (2010)
  • A. L. Fradkov, I. V. Miroshnik, V. O. Nikiforov, Nonlinear and adaptive control of complex systems, Kluwer (1999)
  • A. L. Fradkov, Cybernetical Physics: From Control of Chaos to Quantum Control, Springer, (2007)
  • Eckehard Schöll, Hans Georg Schuster, Handbook of chaos control (Second completely revised and enlarged edition) Wiley (2008)
  • Wolfram Just, Axel Pelster, Michael Schanz, Eckehard Schöll, Delayed Complex Systems: An Overview, Theme Issue of Phil. Trans. R. Soc. A 368, 303 (2010)
  • Lutz Schimansky-Geier, Bernold Fiedler, Jürgen Kurths, Eckehard Schöll, Analysis and control of complex nonlinear processes in physics, chemistry and biology, World Scientific (2007)
  • Thomas Erneux, Applied Delay Differential Equations, Springer (2009)
  • Crispin W. Gardiner, Handbook of stochastic method, Springer (2004)
  • Nicolas G. van Kampen, Stochastic processes in physics and chemistry, North-Holland Publ. (2008)
  • Ruslan L. Stratonovich, Topics in the Theory of Random Noise, Vols. I and II, Gordon and Breach (1963)
  • Ed Ott, Chaos in dynamical systems, Cambridge Univ. Press (2002)
  • Aleksandr S. Mikhailov, Foundations of Synergetics I. Distributed Active Systems, Springer (1990)
  • James D. Murray, Mathematical Biology,Vol. 19 of Biomathematics Texts, Springer (1989)
  • Hermann Haken, Synergetics. Introduction and Advanced Topics, Springer (2004)
  • John Guckenheimer, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer (1986)
  • Steven H. Strogatz, Nonlinear Dynamics And Chaos: With Applications To Physics Biology, Chemistry And Engineering (Studies in Nonlinearity), Westview Press (2000)
  • Jack K. Hale and Sjoerd M. Verduyn Lunel, Introduction to functional differential equations, Springer (1993)
  • Richard Bellman, and Kenneth L Cooke, Differential-difference equations, New York-London: Academic Press. (1963)
  • A. Bellen and M. Zennaro and A. Bellen, Numerical Methods for Delay Differential Equations, Oxford Univ Pr (2003)

Zusatzinformationen / Extras

Quick Access:

Schnellnavigation zur Seite über Nummerneingabe

Auxiliary Functions

This site uses Matomo for anonymized webanalysis. Visit Data Privacy for more information and opt-out options.