Lecture "Nonlinear Dynamics and Complex Networks in the Earth System" - Summer term 2016


Important note: Other then previously announced, the lectures will start in the first week of the semester (21 April) !!!

General Information

Place:   Department of Physics, Humboldt University,  Berlin-Adlershof

Lectures:   weekly,   Thursday 13-15 (ct), starting 21 April (Prof. Jürgen Kurths / Dr. Reik Donner / Dr. Jonathan Donges), room NEW 14 1'12

Tutorials:   bi-weekly,   Thursday 15-17 (ct), starting 28 April (Jasper Franke / Chiranjit Mitra), room NEW 15 1'427

Lecture-ID:   40564 VL

Audience:   open for all students of natural sciences and related areas with particular interest in the physical modeling of climate, ecology and socio-economy (advanced BSc, MSc or PhD student level)

Certificate:   regular participation in lectures and tutorials, presentation of a semester project during the last lecture


Tentative agenda

    • Introduction, Foundations of Dynamical Systems Theory
    • Dynamical Systems and Bifurcations
    • History of Earth Climate and Conceptual Models of Ice Ages
    • Nonlinear Models of Climate Physics
    • Tipping Points in Dynamical Systems
    • Complex Networks: Foundations and Structural Properties
    • Complex Networks: Models
    • Complex Systems in Theoretical Ecology
    • Adaptive Networks: Epidemic Spreading
    • Adaptive Networks: Opinion Formation
    • Co-Evolutionary Models of Nature and Society
    • Empirical Data Analysis using Complex Network Methods


    Specific literature

    Introduction to nonlinear dynamical systems and chaos

    • Strogatz, S. H. (2014). Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Westview Press.
    • Ott, E. (2002). Chaos in dynamical systems. Cambridge University Press.
    • Argyris, J., Faust, G., & Haase, M. (2013). Die Erforschung des Chaos: Studienbuch für Naturwissenschaftler und Ingenieure. Springer-Verlag.
    • Cvitanovic, P., Artuso, R., Mainieri, R., Tanner, G., Vattay, G., & Whelan, N. (2005). Chaos: classical and quantum. ChaosBook.org (Niels Bohr Institute, Copenhagen 2005).

    Nonlinear dynamics and phenomena in the Earth system

    • Dijkstra, H. A. (2013). Nonlinear climate dynamics. Cambridge University Press.
    • Scheffer, M. (2009). Critical transitions in nature and society. Princeton University Press.

    Structure and history of the Earth system

    • Schellnhuber, H.J. & Rahmstorf, S. (2012). Der Klimawandel: Diagnose, Prognose, Therapie, C.H. Beck.
    • Ruddiman, W. (2013). Earth's climate: past and future. W.H. Freeman & Co Ltd.

    Complex networks

    • M.E.J. Newman: Networks - An Introduction. Oxford University Press
    • R. Albert, A.-L. Barabási: Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47, 2002
    • M.E.J. Newman: The structure and function of complex networks. SIAM Review, 45, 167-256, 2003

    Theoretical ecology, epidemic spreading and social dynamics

    • Structural models of food webs: D.B. Stouffer, J. Camacho, R. Guimera, C.A. Ng, L.A. Nunes Amaral, Quantitative patterns in the structure of model and empirical food webs. Ecology, 86, 1301-1311, 2005
    • Types of functional responses in food web models: J.H.P. Dawes, M.O. Souza, A derivation of Holling's type I, II and III functional response in predator-prey systems. Journal of Theoretical Biology, 327, 11-22, 2013
    • Generalized modeling: T. Gross, U. Feudel, Generalized models as a universal approach to the analysis of nonlinear dynamical systems. Physical Review E, 73, 016205, 2006; T. Gross, L. Rudolf, S.A. Levin, U. Diekmann, Generalized models reveal stabilizing factors in food webs. Science, 325, 747-750, 2009; J.D. Yeakel, D. Stiefs, M. Novak, T. Gross, Generalized modeling of ecological population dynamics. Theoretical Ecology, 4, 179-194, 2011
    • Epidemic models on complex networks: P. Pastor-Satorras, A. Vespigniani, Epidemic dynamics and endemic states in complex networks. Physical Review E, 63, 066117, 2001
    • Voter model on networks: F. Vazquez, V.M. Eguiluz, Analytical solution of the voter model on uncorrelated networks. New Journal of Physics, 10, 063011, 2008

    Adaptive networks

    • T. Gross, H. Sayama (eds.): Adaptive networks - Theory, Models and Applications. Springer
    • T. Gross, B. Blasius, Adaptive coevolutionary networks - a review, Journal of the Royal Society Interface, 5, 259-271, 2008
    • G. Demirel, F. Vazquez, G.A. Böhme, T. Gross, Moment-closure approximations for discrete adaptive networks, Physica D, 267, 68-80, 2014

    More references will be added following the progress of the lectures.


    Continuous updates on the tutorials will be posted below.

    Last update:   13 July 2016