Topics in Dynamical Systems: Stochastic Dynamics

What it is about

You deal with stochastic or random dynamical systems. You will learn fundamentals, important methods (e.g. Fokker–Planck approach, large deviations, moment methods) as well as phenomena such as noise-induced behavior, synchronization by noise and stochastic bifurcations; at the end you will be able to analyze a given system with appropriate concepts/algorithms and make qualitative as well as quantitative statements about the dynamics.

What you will be able to do

• Understand fundamental stochastic dynamics
• Apply stability and invariant measure concepts
• Use PDE methods (Fokker–Planck/Kolmogorov)
• Utilize homogenization/averaging and multi-scale methods
• Analyze large deviation principles and noise-induced phenomena
• Assess Lyapunov exponents, MET and stochastic attractors
• Apply stochastic invariant manifolds and bifurcations
• Use simple concepts of rough differential equations and quasi-stationary states

What the module consists of

• VorlesungPresentation of content on the board; introduction to theory, examples and applications
• Tutorium/ÜbungAccompanying exercises with problem sheets; guided sessions with a focus on independent solving

Teaching method

• TafelvorlesungConveying content with room for discussion and in-depth explanations
• Discussion/Encouragement of independent literature workThe goal is that you analyze the topics independently and deepen them further
• Tutorials with problem sheetsPractice and deepening of lecture material through guided but independent problem solving