Towards Understanding Complex Spatio-Temporal Systems
- Thursday, February 25, 2021 from 3:00pm to 4:00pm
- Webex Meeting number: 120 608 6197, Password: applied
Nonlinear dynamical systems play an important role in modeling various processes in fields ranging from physics, chemistry and biology to social sciences. Despite their importance, the global dynamics of many nonlinear systems is still far from being properly understood. Understanding the global dynamics becomes even more challenging if the governing equations are not known and only experimental data are available. In this talk I will introduce rigorous mathematical methods for analyzing the dynamics of a system from data and demonstrate these methods on a variety of different problems which exhibit an intricate pattern formation. In the first part I will explain how persistence homology can be used to describe complex patterns in a concise and informative manner. By imposing different metrics on the space of persistence diagrams we can assess local and global differences between the patterns. Thus, this space is a good observation space to study pattern evolution. In the second part of this talk I will discuss topological methods for identifying robust dynamical structures that act as organizing blocks of the dynamics.
- Department of Mathematical Sciences