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.
- Kursverantwortliche/r: PD Dr. habil. Irina Kmit