Lecture in the summer term 2011

Staff: Dr. Philipp Hövel [1]

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 [2], campus map [3])

For students of the Physics Programme (Master and Diplom-Hauptstudium), the International Master Program Computational Neuroscience [4] as well as interested members of Graduiertenkolleg 1558 (Nonequilibrium Collective Dynamics in Condensed Matter and Biological Systems) [5] and the Sonderforschungsbereich 910 (Control of self-organizing nonlinear systems: Theoretical methods and concepts of application) [6].

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) [7] to a physikalischen Wahlpflichtmodul (grundlagenorientierte Studienrichtung).

Another lecture with the related topic "Nichtlineare Dynamik in Physiologie und Medizin" [8] is given by Dr. Markus Dahlem [9].

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 [10].

Literature concerning the topic of this lecture:

• Claudius Gros: Complex and Adaptive Dynamical Systems: A Primer, Springer (2010)
• Niloy Ganguly: Dynamics On and Of Complex Networks: Applications to Biology, Computer Science, and the Social Sciences (Modeling and Simulation in Science, Engineering and Technology), Springer (2009)
  
• Mark Newman: Networks: An Introduction, Oxford University Press (2010)
  
• Sergey N. Dorogovtsev: Lectures on Complex Networks (Oxford Master Series in Physics, Computational, and Theoretical Physics), Oxford University Press (2010)
• Guido Caldarelli: Scale-Free Networks: Complex Webs in Nature and Technology (Oxford Finance), Oxford University Press (2007)
• Marco Thiel: Nonlinear Dynamics and Chaos: Advances and Perspectives (Understanding Complex Systems), Springer (2010)
  
• Erik Mosekilde: Chaotic Synchronization: Applications to Living Systems (World Scientific Series on Nonlinear Science Series a), World Scientific (2002)
• Christof Koch: Biophysics of Computation: Information Processing in Single Neurons [15], Oxford University Press (1999)
  

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)