Lecture "Nonlinear Dynamics and Complex Networks in the Earth System" - Winter term 2017/18

General Information

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

Lectures:   weekly,   Wednesday 15-17 (ct), starting 18 October (Prof. Jürgen Kurths / Dr. Reik Donner / Dr. Jonathan Donges), room NEW 15 3'101

Tutorials:   bi-weekly,   Wednesday 17-19 (ct), starting 25 October (Jaqueline Lekscha / Jakob Kolb), room NEW 15 3'101

Lecture-ID:   40497 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

    Lecture notes and slides are available for selected lectures and will be distributed to registered participants via email. In addition, there is a (growing) list of recommended books, review articles as well as papers on specific topics that will be listed below.

    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


    Continuous updates on the tutorials will be posted below. 

    Last update:   18 October 2017