Seminar on Qualitative Theory of Differential Equations - Richard Kollár (12.4.2018)
Thursday 12.4.2018 at 14:00 hod., Lecture room M/223
By: Pavol Quittner
Spectral Stability in Reduced and Extended Systems
Spectral stability indicates expected short time evolution of a solution perturbed initially from a relative equilibrium state. It typically determines also nonlinear stability of the solution but any such result is always limited to the exact algebraic formulation of the system. However, governing equations are often only an approximation of the real system that may involve external feedbacks. We show how is the spectral stability of a solution in the reduced system related to the spectral stability in a full (extended) system. As a case study we consider systems of ODEs (quasi-steady-state reduction) and their general embedding of into a larger system. A connection is drawn with geometric Krein signature that surprisingly captures spectral properties under such extensions.