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Stochastic Nonlinear Systems

Module PH2279

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2279 is a semester module in language at which is offered irregularly.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Responsible coordinator of the module PH2279 is Ulrich Gerland.

Content, Learning Outcome and Preconditions


  • Nonlinear dynamics
  • New developments in the analysis of pattern formation of spatially extended systems far from equillibrium
  • Noise induced symmetry breaking far from equilibrium
  • Population dynamics

Learning Outcome

After successful completion of the module the students are able to:

  1. Know and apply basic concepts of nonlinear dynamics
  2. Apply current tools of nonlinear stochastic systems
  3. Analyze pattern formation theoretically with state of the art methods
  4. Understand mechanisms of stochastic symmetry breaking


Basic knowledge of the theory of stochastic processes (equivalent to PH1006) and basic statistical physics is recommended. Knowledge of nonlinear dynamics will be helpful but not necessary.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Stochastic Nonlinear Systems Gerland, U. Tue, 14:00–16:00, PH 3344
UE 2 Exercises to Stochastic Nonlinear Systems Gerland, U. dates in groups

Learning and Teaching Methods

In the thematically structured lecture, the theoretical contents are presented and discussed. The theoretical models for the description of nonlinear stochastic systems are developed on the blackboard together with the students. Concrete physical and biological examples are studied in-depth, and in some cases compared to experimental results.

In the problem sets the students have the opportunity to apply the presented techniques to concrete problem examples and to familiarize themselves with the models of the field.

In the tutor groups (ecercises) the problem sets are discussed. Further questions of students are given a large space. The tutorials provide also a room for discussion and further explanations of topics of the lecture


Lecture notes, problem sheets, web page



  • Crispin Gardiner: "Stochastic Methods: A Handbook for the Natural and Social Sciences" (Springer)
  • N.G. van Kampen: "Stochastic Processes in Physics and Chemistry" (North-Holland)
  • S. Strogatz: Nonlinear Dynamics and Chaos (Westview Press)

Further literature will be announced during the lecture

Module Exam

Description of exams and course work

There will be an oral exam of about 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

  • Explain how moving local equilibria are used to study reaction-diffusion systems!
  • Elucidate how noise can induce chiral symmetry breaking!

In the exam no learning aids are permitted.

Participation in the tutorials is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

Exam Repetition

The exam may be repeated at the end of the semester.

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