Fakultät für Physik
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Nonlinear Dynamics and Pattern Formation – Overview

Lecturer

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Organization of the lecture:

  • Sample solutions for the Trial Exam will be presented during the lectures (February, 8th, 12.00-14.00).
  • If not stated otherwise, the lecture takes place on
    • Tuesday, 10:00 c.t. - 12:00 in room A348, Theresienstr. 37
    • Wednesday, 12:00 c.t. - 14:00 in room B138, Theresienstr. 39
  • Credits: 4 SWS lecture + 2 SWS exercise class, 9 ECTS

 

 Exam

  • Thursday, 23.02.2017 from 10 - 14
  • Room: A348
  • Exam results
  • An opportunity to review the exams will be given on April 6th, 10-12am in room A338.

Topics

  • Bifurcation Theory
  • Excitable Media
  • Evolutionary Game Theory
  • Population Dynamics
  • Pattern Formation
  • Chaos

Perspective

Many systems in nature spontaneously form nontrivial spatial structures: ice flowers on a window or ripples on a beach are simple examples of large scale patterns that occur in nature, but there are also numerous examples of spontaneous pattern formation that occur in non-equilibrium systems in physics, astronomy, chemistry and biology. The behavior of such systems is often highly nonlinear, and hence their description usually involves nonlinear analysis, in particular the analysis of nonlinear partial differential equations. This course will give an introduction to both the phenomena that are encountered, as well as to some of the theoretical models introduced for them and the mathematical techniques needed to analyze their nonlinear behavior.

Literature

  • Nonlinear Dynamics and Chaos, S. H. Strogatz, Westview Press
  • Introduction to Applied Nonlinear Dynamical Systems and Chaos, S. Wiggins, Springer
  • Differential Equations and Dynamical Systems, L. Perko, Springer
  • Pattern Formation and Dynamics in Nonequilibrium Systems, M. Cross and H. Greenside, Cambridge University Press