Seminár z kvalitatívnej teórie diferenciálnych rovníc - Hana Krakovská (24.10.2024)
vo štvrtok 24.10.2024 o 14:00 hod. v miestnosti M 223
Prednášajúci: Hana Krakovská (Medical University of Vienna)
Názov prednášky: Resilience of attractors in dynamical systems
Termín: 24.10.2024, 14:00 hod., M 223
Abstrakt:
While local stability has been extensively studied in dynamical systems theory, assessing "non-local" stability or "resilience", is a challenging task. There are numerous interpretations and definitions of resilience, primarily driven by applied fields, which are often vague. However, to develop a mathematical theory of resilience that can be used across various domains, it is essential to establish precise and rigorous definitions of resilience indicators. In the talk, I will present and analyze the most relevant resilience indicators for the attractors in continuous dynamical systems. Additionally, I will compare the resilience indicators in a classic ordinary differential equation model from population dynamics with the Allee effect, demonstrating that a detailed mathematical analysis leads to direct quantitative comparisons of resilience in different parameter regimes. I will highlight that our analysis reveals different conclusions about the resilience of the attractor depending on which indicator is used. Thus, it is crucial to carefully determine the nature of the perturbations that affect the attractor when posing a resilience question and select an appropriate resilience indicator accordingly.
The talk is based on the paper
Krakovská H, Kuehn C, Longo IP: Resilience of dynamical systems.
European Journal of Applied Mathematics 35 (2024), 155-200.