Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 12.4.2018 at 14:00 Lecture room M-223

Richard Kollár (KAMŠ FMFI UK):

Spectral Stability in Reduced and Extended Systems

Abstract:

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.