Seminar: Introduction to Nonlinear Dynamics

Dr. habil. Irina Kmit

Time & Place

Wednesday: 15:00-17:00 (weekly)

Rudower Chaussee 25, room 1.011

Short description

Dynamic systems model  phenomena and processes  changing over time and described by  differential equations. In this seminar we will discuss questions  about how dynamical systems evolve  over time, which  states they exhibit and how sensitive they are to  parameters and initial conditions. Nonlinear dynamics covers phenomena varying from weather patterns formation  to neural networks, from physics and engineering to biology and economics.

Key topics  of the seminar:

• Basic  concepts of solutions to linear and nonlinear  systems of ordinary differential equations.

• General features of dynamical systems: asymptotic behavior, stability, classification.

• Stability of dynamical systems: Lyapunov  and asymptotic stability.

• Linerization and hyperbolicity. The existence and stability of fixed points, periodic orbits and other types of solutions.

• Changes of the qualitative behavior when  the parameters vary (structural stability, bifurcations, chaos). 

Prerequisites

Analysis  III; Linear Algebra II. 

Seminar talks

Every participant will be asked to give a 70-minute presentation.

References

• • Steven H. Strogatz. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Taylor & Francis, 2018.

  • Paul Glendinning. Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations. Cambridge Texts in Applied Mathematics, 1994.