Intendierte Lernergebnisse
To be able to analyze qualitative behavior of dynamical systems using various notions and tools of Nonlinear Dynamics and Stability Theory.
Lehrmethodik
Lecture, discussion, examples
Inhalt/e
The course focuses on the study of dynamical systems governed by nonlinear ordinary differential equations. We will consider some fundamental concepts of the theory of nonlinear dynamical systems and discuss their applications in areas ranging fromcontrol theory and mechanics. The main topics are:Elements of nonlinear ODEs Lyapunov stability BifurcationsCenter manifoldsElements of dynamical control systems
Erwartete Vorkenntnisse
Analysis, Linear Algebra, Ordinary Differential Equations
Literatur
V.I. Arnold. Ordinary Differential Equations.J. Guckenheimer, P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcationsof Vector Fields.H. Khalil. Nonlinear Systems.H. Nijmeijer , A. van der Schaft. Nonlinear Dynamical Control Systems.S. Sastry. Nonlinear Systems.