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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.

Contents

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

Scheinkriterien

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

e-learning

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

Exercise Sheets

Title
Due date
File
Network characteristics
Graph theory
10.6.2011
Uebung1.pdf
SIS model
17.6.2011
Ubeung2.pdf
Reaction-diffusion, Master stability function formalism
24.6.2011
Uebung3.pdf

Office hours

Name
Phone
Room
Office hours


314-27658
TU Berlin: EW 633
Tue: 13:00 - 14:00
2093-6313
BCCN: 0.24 (Haus 2)
by appointment

Literature

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)

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