Minisymposium: Realization of connection structures in phase space

Abstract

Together with Alexander Lohse, I am co-organizing the minisymposium “Realization of connection structures in phase space” at the Dynamics Days Europe 2024.

Complex systems in applications ranging from ecology to game theory display dynamic transitions between different (quasi-)invariant states. A well-known example are fluctuations of species abundancies in ecosystems. When more than two such states are present, not all transitions are necessarily possible and intriguing patterns may emerge in the connection structure. These transitions can be modeled e.g. as heteroclinic or excitable connections between (quasi-)invariant sets. Recent years have seen remarkable developments when it comes to realizing specific transition structures—given by a directed graph—as dynamical structures in the phase space of an ODE system. Oftentimes, additional restrictions are to be met: for instance, additional dynamical properties such as robustness or stability might be desirable for the connection structure. On the other hand, the class of vector fields in which the design takes place can be restricted for example by underlying symmetries or coupling structure.

This minisymposium brings together leading experts in the area of restricted design to discuss recent advances and to uncover potential future paths.

Sören von der Gracht

PostDoc in Dynamical Systems

Research in network dynamical systems and its applications.