University of São Paulo, Brazil
Title: Quiver symmetries in network dynamical systems
Abstract: Many coupled cell systems show highly unusual dynamical behavior as a generic phenomenon. Examples include invariant (synchrony) spaces, eigenvalue degeneracy and elaborate synchrony-breaking bifurcations. These are all observed –and quite well-understood– in systems with finite group symmetry, though many examples exist of non-symmetric networks with the same anomalous behavior. We present a vast generalisation of this classical set-up, where the symmetry maps need not be invertible and may map between different dynamical systems. These so-called quiver symmetries allow for an equivalent description of many forms of network structure, and capture even more geometric features, such as the presence of invariant synchrony spaces, subnetworks, hidden symmetry, and so forth. We then show that quiver symmetry may be preserved in various complexity reduction techniques, thus developing dynamical techniques that are tailor-made for networks. This is based on joint work with Sören von der Gracht and Bob Rink.
Bio: CV