Stochastic Nonlinear Systems

• 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

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.

The module cosists od a lecture and exercise classes. 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 ecercises the problem sets are discussed. Further questions of students are given a large space. The exercises provide also a room for discussion and further explanations of topics of the lecture

Lecture notes, problem sheets, web page

• C. Gardiner: Stochastic Methods: A Handbook for the Natural and Social Sciences, Springer, (2009)
• N.G. van Kampen: Stochastic Processes in Physics and Chemistry, North-Holland, (2007)
• S.H. Strogatz: Nonlinear Dynamics and Chaos, Westview Press, (2014)

There will be an oral exam of 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!
• What methods are used for pattern formation analysis?

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.