Homogeneous coupled cell systems - unexpected symmetries and how to exploit them in bifurcation analysis

Room FC1.031
Friday, 22 June, 2018 - 14:30

Dynamical systems with an underlying network structure are a subject of great interest as they arise frequently in applications and exhibit many staggering phenomena some of which resemble those in equivariant dynamics. We introduce a theory developed by Rink and Sanders that connects a class of network dynamical systems - namely homogeneous coupled cell systems - to equivariant dynamical systems. The symmetries, however, are generalized in the sense that they do not necessarily form a group but more general structures such as monoids or semigroups. We investigate how to exploit these symmetries in order to understand the generic bifurcation behavior of a given network. Finally we present some ideas and open questions on how to exploit representation theory of finite monoids in order to further deepen the understanding of networks.



Sören Schwenker


Universität Hamburg, Germany