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(Exercises: WS2005, WS2004, WS2003, WS2002)



 1. Nonlinear dynamics I & II

 2. Characterization of discrete and continuous nonlinear deterministic dissipative
    dynamical systems: Attractors, deterministic chaos, fractal dimensions, Lyapunov
    exponents, entropies, bifurcations. routes to chaos. universal constants, 
    influence of random noise. synchronization. stochastic resonance. coupled maps.
    Spatially extended systems: instabilities and pattern formation, reaction-diffusion
    equations, universal model equations (e.g. Ginzburg-Landau equation).
    Prototypical examples of corresponding systems in physics, biology and Earth science.

 3. Admission requirements:
    intermediate examination

 4. Optional compulsory course

 5. Prof. Dr. Arkadi Pikovski, Prof. Dr. Matthias Holschneider, Dr. Udo Schwarz

 6. Credit weighting:
    6 SWS all 
    4 SWS lecture
    2 SWS practical

 7. Lecture and practical

 8. Course assessment:
    Solve exercises, written examination 

 9. German and English

 10. 9 ECT-points all

 11. Literature:
Kaplan & Glass: Understanding nonlinear dynamics . 1958/1965
S.H. Strogatz: Nonlinear dynamics and chaos : with applications to physics, biology, chemistry, and engineering. Cambridge, Mass: Perseus Books, 2001
R.W. Leven, B.-P. Koch, B. Pompe: Chaos in dissipativen Systemen. Akademie-Verlag, Berlin 1989, 1994
J. Argyris, G. Faust & M. Haase: Die Erforschung des Chaos. Vieweg, Braunschweig, 1994
Heinz-Otto Peitgen, Hartmut Jügens, und Dietmar Saupe: Bausteine des Chaos. Fraktale. 1998.
Heinz-Otto Peitgen, Hartmut Jürgens, und Dietmar Saupe: Chaos. 1998.
H.K. Khalil: Nonlinear systems. Prentice Hall 2002
R.C. Robinson: An Introduction to Dynamical Systems: Continuous and Discrete. Prentice Hall 2004
Willi-Hans Steeb: THE NONLINEAR WORKBOOK Chaos, Fractals, Cellular Automata, Neural Networks, Genetic Algorithms, Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic with C++, Java and SymbolicC++ Programs. World Scientfic, 2008
Andronov, Vitt, Chajkin, Semen: Theory of oscillators. Dover 1966
Bogoljubow & Mitropolski: Asymptotische Methoden. 1958/1965
Aggarwal: Notes on nonlinear systems. 1972
Hagedorn: Non-linear oscillations. 1978
Percival & Richards Introduction to dynamics. 1982
Zaslavsky G M: Stochastische dynamische Systeme. 1984
Zaslavsky G M: Hamiltonian chaos & fractional dynamics . 1984
Lichtenberg, Allan J. & Lieberman, Michael A. Regular and chaotic dynamics. 1992
Haake, Fritz: Quantum signatures of chaos. Springer, 2001
Landa: Nonlinear Oscillations and Waves in Dynamical Systems. 2001
George M. Zaslavsky: Hamiltonian chaos and fractional dynamics. 2008
Jose & Saletan: Classical Dynamics. Cambridge University Press, 1998.
Haberman: Mathematical Models. 1998
P. Cvitanovic, R. Artuso, P. Dahlqvist, R. Mainieri, G. Tanner, G. Vattay, N. Whelan & A. Wirzba: Nonlinear Dynamics eBook
M. Lakshmanan & S. Rajasekar: Nonlinear dynamics: integrability, chaos, and patterns. Springer, Berlin, 2003
P. Glendinning: Stability, Instability and Chaos : An Introduction to the Theory of Nonlinear Differential Equations, Cambridge Univ. Press, 1996
P.G. Drazin: Nonlinear Systems, Cambridge UP 1997
P. Plaschko & K. Brod: Nichtlineare Dynamik, Bifurkation und Chaotische Systeme. Vieweg, Braunschweig 1995
V. Reitmann: Nichtlineare Dynamik. Teubner, Stuttgart 1996
H.G. Schuster: Deterministisches Chaos: eine Einführung. VCH, Weinheim 1994
Haken: Synergetik. Springer 1977
Ebeling, Engel, Herzel: Selbstorganisation in der Zeit. Akademie 1990
Ebeling & Feistel: Physik der Selbstorganisation. Akademie 1982
Minorsky, Nicholas: Nonlinear Oscillations. Van Nostrand, 1962
Srensen, Christiansen, Scott: Nonlinear Science: Emergence and Dynamics of Coherent Structures. Oxford University Press
R. Hoyle: Pattern Formation An Introduction to Methods.. Cambridge UP 2006
Script

(WS2004, WS2003, WS2002)

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